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CBSE Economics Chapter 4 Presentation of Data class 11 Notes Economics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Presentation of Data class 11 Notes Economics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Economics notes on Chapter 4 Presentation of Data class 11 Notes Economics are also available for download in CBSE Guide website.

CBSE Guide Presentation of Data class 11 Notes

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Download CBSE class 11th revision notes for Chapter 4 Presentation of Data class 11 Notes Economics in PDF format for free. Download revision notes for Presentation of Data class 11 Notes Economics and score high in exams. These are the Presentation of Data class 11 Notes Economics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

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CBSE Class 11 Economics Revision Notes Chapter – 4 Presentation of Data class 11 Notes Economics

The presentation of data means exhibition of data in such a clear and attractive manner that these can be easily understood and analysed.

Forms of Presentation of data: 1. Textual/Descriptive Presentation 2. Tabular Presentation 3. Diagrammatic Presentation 4. Graphical Presentation

1. Textual/Descriptive Presentation of Data:- In this, data is presented in the form of text. This is suitable when quantity of data is not too large.

2. Tabulation – It is the process of presenting data in the form of a table. Parts or components of Table: 1. Table Number 2. Title 3. Caption Or Column Headings 4. Stubs Or Row Headings 5.  Body of the Table 6. Unit of Measurement 7. Source 8. Head Note 9. Foot Note

Features of a good table: (a) Compatible with the objective (b) Helpful in comparison (c) Ideal Size (d) Stubs (e) Headings (f) Percentage and ratio (g) Sources of Data (h) Simplicity

Kinds of Table: 1. According to Purpose 2. According to originality 3. According to construction

Classification of tabular presentation of data 1. Qualitative Classification:- When classification is done according to attributes such as social status, nationality, etc. It is called qualitative classification. 2. Quantitative Classification:- In this, the data are classified on the basis of characteristics which are quantitative in nature. e.g., age, height, income, etc. 3. Temporal classification:- In this, time becomes the becomes the classifying variable and data are categorised according to time. Time may be in hours, weeks, years, etc. 4. Spatial classification:- When classification is done on the basis of place, it is called spatial classification. The place may be village, town, state, country, etc.

Diagrammatic Presentation : When data is presented in a simple and attractive manner in the form of diagrams is called diagrammatic presentation of data.

Types of Diagrammatic Presentation : 1. Geometric Form a. Pie Diagram b. Bar Diagram i. Simple ii. Multiple iii. Sub Divided iv. Percentage

2. Frequency Diagram a. Histogram b. Frequency Polygon c. Frequency Curve d. Ogive curve

3. Arithmetic Line Graph or Time series graph 1. Bar diagram:-  Bar diagrams are those diagrams in which data are presented in the form of bars or rectangles. Simple bar diagram:- They are those diagrams which are based on a single set of numerical data. Different items are represented by different bars. Multiple bar diagram:- They are those diagrams which show two or more sets of data simultaneously. This type of diagram is, generally, used to make comparison between two sets of series. Sub divided bar diagram:- These are those diagrams which present simultaneously, total values and parts there in a set of a data. Percentage bar diagram:-  They are those diagram which show simultaneously different parts off the values of a sets of data in terms of percentage. Deviation bar diagram:-  These are used to compare the net deviation of related variables with respect to time and location. Bars which represent positive deviation and which represent negative deviation are drawn above and below the base line respectively. Pie or circular diagram is a circle divided into various segments showing the per cent values of a series. Histogram is graphical presentations of a frequency distribution of a continuous series.It can never be drawn for a discrete series. Frequency polygon is drawn by joining the mid points of the tops of rectangles in a histogram. It is constructed with the help of discrete as well as continuous series. Frequency curve is obtained by joining the points of a frequency polygon through free hand smooth curve not by straight lines. Cumulative frequency curves or ogive curve is the curve which is constructed by plotting cumulative frequency data on the graph paper in the form of a smooth curve. Arithmetic line Graphs or Time Series Graphs:-   In this graph, time(hour,day, date, week, month, year) is plotted along X-axis and the  corresponding value of variable along Y-axis.

Presentation of Data class 11 Notes

• CBSE Revision notes (PDF Download) Free
• CBSE Revision notes for Class 11 Economics PDF
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• Summary of the NCERT books all chapters in Economics class 11
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• Quick revision notes for CBSE exams

CBSE Class-11 Revision Notes and Key Points

Presentation of Data class 11 Notes Economics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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To download Presentation of Data class 11 Notes, sample paper for class 11 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through  the best app for CBSE students  and myCBSEguide website.

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1.3: Presentation of Data

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Learning Objectives

• To learn two ways that data will be presented in the text.

In this book we will use two formats for presenting data sets. The first is a data list, which is an explicit listing of all the individual measurements, either as a display with space between the individual measurements, or in set notation with individual measurements separated by commas.

Example \(\PageIndex{1}\)

The data obtained by measuring the age of \(21\) randomly selected students enrolled in freshman courses at a university could be presented as the data list:

\[\begin{array}{cccccccccc}18 & 18 & 19 & 19 & 19 & 18 & 22 & 20 & 18 & 18 & 17 \\ 19 & 18 & 24 & 18 & 20 & 18 & 21 & 20 & 17 & 19 &\end{array} \nonumber \]

or in set notation as:

\[ \{18,18,19,19,19,18,22,20,18,18,17,19,18,24,18,20,18,21,20,17,19\} \nonumber \]

A data set can also be presented by means of a data frequency table, a table in which each distinct value \(x\) is listed in the first row and its frequency \(f\), which is the number of times the value \(x\) appears in the data set, is listed below it in the second row.

Example \(\PageIndex{2}\)

The data set of the previous example is represented by the data frequency table

\[\begin{array}{c|cccccc}x & 17 & 18 & 19 & 20 & 21 & 22 & 24 \\ \hline f & 2 & 8 & 5 & 3 & 1 & 1 & 1\end{array} \nonumber \]

The data frequency table is especially convenient when data sets are large and the number of distinct values is not too large.

Key Takeaway

• Data sets can be presented either by listing all the elements or by giving a table of values and frequencies.

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Statistics for Economics Class 11 Notes Chapter 4 Presentation of Data

July 5, 2019 by Sastry CBSE

Textual Presentation In textual presentation, data are a part of the text of study or a part of the description of the subject matter of study.

Tabular Presentation of Data “Tabulation involves the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration”

Components of a Table Following are the principal components of a table

• Table number
• Body or field

Classification of Data and Tabular Presentation (i) Qualitative Classification of Data and Tabular Presentation Qualitative classification occurs when data are classified on the basis of qualitative attributes or qualitative.

(ii) Characteristics of a Phenomenon

• Quantitative Classification of Data These occurs when data are classified on the basis ot quantitative characteristics of a phenomenon.
• Temporal Classified of Data In this, data are classified according to time, and time becomes the classifying variable.

(iii) Spatial Classification In spatial classification place, location becomes the classifying variable. It may be a village, a town, a district, etc. (iv) Merits of Tabular Presentation

• Simple and brief presentation
• Facilitates comparison
• Easy analysis
• High lights characteristics of data

Diagrammatic Presentation of Data These translates quite effectively the highly abstract ideas contained in numbers into more concrete and easily comprehensible form. Diagrammatic presentation is classified as given below (i) Bar Diagrams Bar diagrams are these diagrams in which data are presented in the form of bars or rectangles. Types of Bar Diagram are as follows

• Simple Bar Diagrams Simple bar diagrams are those diagrams which are based on a single set of numerical data.
• Multiple Bar Diagrams These are those diagram which show two or more sets of data simultaneously.
• Sub Divided Bar Diagram Sub-divided bar diagram are those diagrams which simultaneously present total values as well as part values of a set of data.
• Percentage Bar Diagram Percentage bar diagrams are those diagrams which show simultaneously, different parts of the values of a set of data in terms of percentages.

(ii) Pie or Circular Diagrams Pie diagram is a circle divided into various segments showing the per cent values of a series. This diagram does not show absolute values. (iii) Frequency Diagram Data in the form of grouped frequency distributions are generally represented by frequency diagram like histogram, frequency polygon, frequency curve and ogive.

• Histogram of equal class intervals
• Histogram of unequal class intervals
• Polygon Polygon is another form of diagrammatic presentation of data. It is formed by joining mid points of the tops of all rectangles in a histogram. However, a polygon can be drawn even without constructing a histogram.
• Frequency Curve A frequency curve is a curve which is plotted by joining the mid points of all tops of histogram by free hand smoothed curves and not by straight lines.
• Less than Method In this method, beginning from upper limit of the 1st values we go on adding the frequencies corresponding to every next upper limit of the series.
• More than Method In this method, we take cumulative total of the frequencies beginning with lower limit of the 1st class interval.

(iv) Arithmetic Line Graph An arithmetic line graph is also called time series graph. In it time is plotted along x-axis and the value of the variable along y-axis. A line graph by joining these plotted points, these obtained is called time series graph.

Rules for Constructing a Graph

• Choice of scale
• Proportion of axis
• Method of plotting the points
• Lines of different types
• Table of data
• Use of false line
• One Variable Graph One variable graph are those graphs in which values of only one variable are shown with respect to some time period.
• Two or More than Two Variable Graphs These – are the graphs in which values of two variables are simultaneously shown with respect to some period of time.

Merits of Diagrammatic and Graphic Presentation

• Simple and understandable information
• Lasting impact
• No need of training or specialised knowledge
• Attractive and effective means of presentation
• A quick comparative glance
• Information and entertaining
• Location of averages
• Study of correlation

Limitations of Diagrammatic and Graphic Presentation

• Limited use
• Only preliminary conclusions

Statistics for Economics Class 11 Notes

Class 11 economics notes, free resources.

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Presentation of Data Class 11 Notes PDF (Handwritten & Short Notes)

In the Presentation of Data class 11 notes, topics and concepts are explained in a creative manner, accordingly students can also improve their creativity. With this, students can also attempt questions of Presentation of Data in an innovative way as it encourages them to engage in understanding complex topics in an ease. 

The Presentation of Data class 11 notes can be useful for both teachers and students as it is arranged in a systematic manner so they can easily evaluate their progress and quickly cover the chapter. The systematic organisation can also help students to overcome unnecessary disturbances while completing the Statistics for Economics chapter Presentation of Data. 

Presentation of Data Class 11 Notes PDF

Students can utilise the Presentation of Data class 11 notes PDF while preparing for the chapter from their comfort zone. As they can go through the PDF of class 11 notes from the Selfstudys website so that they can quickly cover Presentation of Data and can understand the chapter in a better way. 

Where Can You Find a Presentation of Data Class 11 Notes?

Students can find the Presentation of Data class 11 notes from the Selfstudys website, steps to download are: 

• Visit the Selfstudys website.
• Click NCERT Books & Solution from the navigation bar. 
• A drop down will appear, select NCERT notes from the given list.

• A new page will appear, select class 11th from the list of classes.

• Select Statistics for Economics from the list of subjects.

• Now select the chapter Presentation of Data from the given list. 

Characteristics of Presentation of Data Class 11 Notes

In the Presentation of Data class 11 notes, some of the definitions are explained in a brief way, other characteristics are: 

• Formulas are Given: The Presentation of Data notes provides important formulas for student’s understanding, accordingly one can solve all types of questions. 
• Flow Charts are Given: A flow chart is a diagram which helps students to understand tough concepts of Presentation of Data.
• Attractive Format: The Presentation of Data class 11 notes PDF are explained in an attractive format so that students can be more attentive towards the chapter. 
• Diagrams are Given: Class 11 Statistics Presentation of Data notes provides diagrams: symbolic representation, so that students can simplify complex content into easier ones. 
• For All Students: All students studying in CBSE and other state boards can look through the Presentation of Data class 11 Economics notes as it is created according to the latest syllabus. 
• Readers Friendly: The notes of Presentation of Data class 11 are user friendly so that students can easily access and learn the concepts. 

Why Should You Use a Presentation of Data Class 11 Notes PDF?

Students should use Presentation of Data class 11 notes PDF so that they can provided with major benefits, those benefits are: 

• Helps in Organisation: The notes of Presentation of Data class 11 keeps students organised about their preparation of the chapter, accordingly they can increase their productivity. 
• Provides an Outline: The notes on Presentation of Data provides an outline for students so that they can get a clarity about concepts of the chapter. 
• Helps in Revising: It is important for students to revise concepts to score good marks, they can recall from the class 11 statistics notes Presentation of Data. 
• Improves Attention Span: The class 11 Statistics notes Presentation of Data helps students to improve their attention span towards the chapter so that they can learn the concepts in a better way. 
• Get an Idea About High Weightage Topics: With the help of Presentation of Data class 11 notes, students can get an idea about the high weightage topics so that they can prepare accordingly. However, these details are not given directly in the notes, but one can refer to the previous year question papers to understand them better.
• Improves Memory: The Presentation of Data class 11 notes PDF helps students to improve their memorisation skills so that they can solve problems within the given time limit. 

When is the Right Time to Go Through The Presentation of Data Class 11 Notes?

Generally, students can go through the Presentation of Data class 11 notes after completing the chapter from NCERT book as it is considered to be the right time. Because in the class 11 notes, topics and concepts of Presentation of Data are explained in a better approach so that students can solve all their doubts as well as confusions.

When to Use the Presentation of Data Class 11 Notes While Preparation? 

Students can totally depend on the Presentation of Data class 11 notes while preparing for the exam, crucial ways that one can depend on the notes are: 

• Class Room Study: Students can go through the Presentation of Data notes during classroom study as it provides a general plan of topics and concepts.
• Weekly Revision: Students can look through the Presentation of Data class 11 notes PDF during weekly revision so that they can clarify doubts on a weekly basis. 
• During Board Exam: Before the board exam, students have to revise all topics so that they can also focus on weaker topics. Accordingly, students can improvise their marks in questions related to Presentation of Data. 
• During Weekly Test: Some students regularly take weekly tests to evaluate their preparation, and can utilise the notes on Presentation of Data so that they can remember the important formulas on their fingertips. 
• Last Minute Preparation: Students generally have the habit of completing the topics during the last minute, so it is better for them to use the Presentation of Data class 11 notes PDF as it can ease their preparation. 

Tips to Prepare for Presentation of Data With The Help of Class 11 Statistics for Economics Notes

Students can follow strategy tips to prepare for Presentation of Data with the help of Class 11 Statistics for Economics Notes , those important tips are: 

• Go Through the NCERT Book: To start the preparation, students need to first go through the Presentation of Data chapter in NCERT book and can also take the help of class 11 Statistics for Economics notes to cover the lesson. 
• Use Mannerism: Students need to create their own tricks: flow charts, diagrams and mannerism to complete Presentation of Data so that they can improve their creativity to complete the notes. 
• Practise Questions: Students are advised to practise questions of the chapter, they can take the help of Presentation of Data notes so that they can understand the concepts in a better way. 
• Make Important Points: While completing the chapter, students can take the help of Presentation of Data notes to make a note of important points in their notebook. 
• Select Study Schedule: Every student has their own comfortable time to complete the notes on Presentation of Data in which their productivity is high.
• Don’t Cram: Students don’t need to cram the topics, it is important for them to understand each and every topic, they can take the help of notes of Presentation of Data class 11.

How to Make the Preparation Effective While Completing Presentation of Data Class 11 Notes?

Effective preparation with the help of Presentation of Data is the key to good score, tips to make the preparation effective are: 

• Form a Proper Routine: Students need to form a proper routine to complete Presentation of Data notes so that they can complete quickly and can also increase their efficiency. 
• Take Intervals: Students are advised to take frequent intervals: listen to music, short walk, snack time to complete Presentation of Data class 11 notes PDF so that they can promote efficiency. 
• Concentration on One Topic: While completing class 11 Economics notes, students need to concentrate on just one topic, this can improve their efficiency to complete Presentation of Data. 
• Update Learning Style: Students need to update their learning style: way of learning on a regular basis to complete class 11 statistics Presentation of Data notes so that they can improve their efficiency. 
• Utilise the Time: Students need to complete the notes of Presentation of Data class 11 without wasting much time in other things can help increase the efficiency. 
• Solve Doubts: It is normal for students to come up with some doubts regarding Presentation of Data as it is important for them to clear their doubts so that they can improve their productivity. 

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Presentation of Data Class 11 Notes: CBSE 11th Economics Chapter 4, Download PDF

Cbse class 11 presentation of data   revision   notes: find here handwritten revision notes for cbse class 11 economics chapter 4, presentation of data. a pdf download link is also available for the same, at the bottom of the article..

Presentation of Data Class 11 Revision Notes: In this article, students can find complete Revision Notes for CSBE Class 11 Economics Chapter 4, Presentation of data. Entire notes have been prepared according to the updated CBSE Syllabus 2023-2024.

Presentation of data teaches students about the power of visualization. How data can be represented in a manner such that it becomes understandable, informative, and interesting at the same time. Economists use multiple forms of representation to showcase different types of data. Each of the forms is explained in detail here so that it becomes easier for students to present data in different forms, as per the requirement.

This article also presents links to other important study materials for Class 11 students. Links to the updated CBSE Class 11 Syllabus are also attached below for your reference.

CBSE Class 11 Economics Syllabus 2023-2024(PDF)

CBSE Class 11 Economics Deleted Syllabus 2023-2024(PDF)

Revision Notes for CBSE Class 11 Economics Chapter 1 2023-2024(PDF)

Revision Notes for CBSE Class 11 Economics Chapter 2 2023-2024(PDF)

Revision Notes for CBSE Class 11 Economics Chapter 3 2023-2024(PDF)

Revision Notes for Class 11 Economics Chapter 4 are presented below:

Presentation of Data - Since data is complex and voluminous, it has to be presented in a manner such that the data becomes understandable and presentable.

Forms of Presentation :

1.Textual or Descriptive Presentation - In this form of presentation, data are described within the text. It is suitable when the quantity of data is not too large. The benefit of using this form is that it gives room for explanation of all relevant data and a disadvantage is that person has to go through every single line for conclusion.

• Qualitative Classification - When classification is done according to attributes, such as social status, physical status, nationality, etc., it is called qualitative classification.
• Quantitative Classification - When classification is done on the basis of characteristics that are quantitative in nature is called quantitative classification.
• Temporal Classification : In this classification, time becomes the classifying variable and data are categorized according to time. Time may be in hours, days, weeks, months, years, etc.
• Spatial Classification : When classification is done on the basis of place, it is called spatial classification. The place may be a village/tow
• Table Number - A table number is assigned to a table for identification purposes. If more than one table is presented, it is the table number that distinguishes one table from another. It is given at the top or at the beginning of the title of the table. Generally, table numbers are whole numbers in ascending order if there are many tables in a book.
• Title - It narrates the contents of the table. It has to be clear, brief, and carefully worded so that the interpretations made from the table are clear and free from ambiguity. It finds a place at the head of the table succeeding the table number or just below it.
• Captions or Column Headings - At the top of each column in a table a column designation is given to explain the figures of the column. This is called a caption or column heading.
• Stubs or Row Headings - Like a caption or column heading, each row of the table has to be given a heading. The designations of the rows are also called stubs or stub items, and the complete left column is known as the stub column.
• Body - The body of a table is the main part and it contains the actual data. The location of any one figure/data in the table is fixed and determined by the row and column of the table.\
• Unit of Measurement - Units of measurement must be stated along with the title. If different units are there for rows or columns of the table, these units must be stated along with ‘stubs’ or ‘captions.
• Source - It is a brief statement or phrase indicating the source of data presented in the table. If more than one source is there, all the sources are to be written in the source. The source is generally written at the bottom of the table.
• Note - Note is the last part of the table. It explains the specific feature of the data content of the table which is not self-explanatory and has not been explained earlier.
• Geometric diagram - A bar diagram and a pie diagram are the two types of geometric diagrams. The bar diagram comprises a group of equispaced and equiwidth rectangular bars for each class or category of data. Height or length of the bar reads the magnitude of data. Bar diagrams are further categorized into simple bar diagrams, multiple bar diagrams, and component bar diagram. A pie diagram is also a component diagram, but unlike a bar diagram, here it is a circle whose area is proportionally divided among the components.
• Frequency diagram - Data in the form of grouped frequency distributions are generally represented by frequency diagrams like histograms, frequency polygons, frequency curves, and ogive.
• Arithmetic line graph - An arithmetic line graph is also called a time series graph. In this graph, time(hour, day/date, week, month, year, etc.) is plotted along the x-axis and the value of the variable (time series data) is along the y-axis.

This chapter is comparatively short and easier to grasp. These notes shall be enough for your preparation for the annual examinations.

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• Economics /

Class 11 Collection, Organisation and Presentation of Data

• Updated on  
• Jun 22, 2023

The collection of data aims to collect evidence for attaining a sound and comprehensible solution to a problem. To understand the inconsistencies in the output, we need the ‘data’ on the generation. It is a process which is conducted to measure and gather information. ‘Data’ is a device, which aids in the comprehension of problems by providing knowledge. Here is this blog, we will talk in detail about the Class 11 collection, organisation and presentation of data. 

Must Read: Business Services Class 11 Notes

This Blog Includes:

What are the sources of data, primary data, secondary data, preparation of instrument, mode of data collection, personal interviews, mailing questionnaire, telephone interviews, pilot survey, census and sample surveys, census , random sampling, non-random sampling, sampling errors, non-sampling errors, census of india and nsso.

To understand more about the chapter Class 11 collection, organisation and presentation of data, we fist need to know the sources of data. Statistical data can be obtained from two sources:

• Primary data

We further move on to the concept of primary data in class 11 collection, organisation and presentation of data. The important points of primary data are:

• The enumerator (person who assembles the data) may collect the data by administering an inquiry or research. Such data is called Primary Data , as it is formulated on first-hand information.
• Primary data are unique, do not require any modification, and are costly.

Next important form of data in class 11 collection, organisation and presentation of data is secondary data.

• If the data have been examined and analyzed by another agency, they are called Secondary Data . Usually, the issued data are secondary.
• They are already in the presence and therefore are not unique.
• It demands to be modified to satisfy the aim of the study at hand.
• Secondary data are low priced.

How do we collect Data?

Collection of data is important in class 11 collection, organisation and presentation of data. It is done by the following ways:

• The survey aims to describe characteristics like cost, worth, utility (in case of the product) and reputation, honesty, loyalty (in case of the nominee).
• The objective of the survey is to gather data and is a method of gathering information from individuals.

The most prevalent type of tool employed in surveys is a questionnaire/ interview schedule. The questionnaire is either self-directed by the interviewee or conducted by the enumerator or qualified investigator. While drawing-up the questionnaire/interview schedule, the following points should be kept in mind:

• The questionnaire should not be lengthy.
• The array of problems should move from indefinite to distinct.
• Questions should not be enigmatic.
• Questions should not use binary negatives. 
• Questions should not be leading.
• Questions should not indicate choices. 

Also Read: Emerging Modes of Business Class 11 Notes

The next important topic in class 11 collection, organisation and presentation of data is the mode of data collection. The aim of probing questions is to survey the acquisition of data. There are three ways of collecting data: 

• Mailing (questionnaire) Surveys

Personal interviews form an important part of the mode of data collection in class 11 collection, organisation and presentation of data. In this method, the researcher has the main role as he/she conducts the interviews face-to-face with the respondents. Personal interviews are preferred due to various reasons:

• Highest Response Rate 
• Allows use of all types of questions 
• Better for using open-ended questions 
• Allows clarification of ambiguous questions.

The personal interview has some demerits too:

• Most expensive 
• Possibility of influencing respondents 
• More time taking

Another important part of class 11 collection, organisation and presentation of data is the mailing questionnaire. In such a method, the data is collected through the mail. The questionnaire is mailed to each person and a  request is attached to complete and return it on time. 

The advantages of this method are:

• Least expensive 
• The only method to reach remote areas 
• No influence on respondents 
• Maintains anonymity of respondents 
• Best for sensitive questions

The disadvantages of mail surveys are:

• Cannot be used by illiterates 
• Long r esponse time  
• Does not allow an explanation of unambiguous questions  
• Reactions cannot be watched 

In telephone interviews, the investigator asks questions over the telephone. 

The advantages of telephone interviews are:

• Relatively low cost 
• Relatively less influence on respondents 
• Relatively high response rate.

The disadvantages of this method are:

• Limited use 
• Possibility of influencing respondents

Explore: Accountancy Class 11 NCERT Solutions

The pilot survey is another important tool in class 11 collection, organisation and presentation of data.

• After the questionnaire is ready, it is desirable to carry a try-out with a diminutive group, known as Pilot Survey or Pre-Testing of the questionnaire . 
• The pilot survey serves to give a preliminary impression of the survey. 
• It helps to pretest the questionnaire and know the lapses and drawbacks.
• It also aids to assess the appropriateness of questions, the accuracy of guidance, the administration of enumerators, and the expense and time required in the actual survey.

Census and sample surveys are an important tool in class 11 collection, organisation and presentation of data. 

• A survey, which encompasses every component of the population, is apprehended as Census or the Method of Complete Enumeration.
• The primary feature of this approach is that this comprises every individual unit in the whole population.

Sample Survey

• A sample refers to a section of the population from which information has to be taken. A good sample (representative sample) is usually short and competent in giving reasonably accurate information about the population at a lower cost and in less time.
• Most of the surveys are sample surveys and are preferable in statistics because of several reasons.
• A sample can give rationally secure and authentic information at a lower cost and in less time. 
• Now the question is how do you do the sampling? There are two main types of sampling:
• Non-random Sampling
• It is also known as the lottery method.
• Random sampling is where the specific units from the population (samples) are randomly selected. 
• In random sampling, each person has an equal possibility of being chosen, and the person who is selected is the same as the one who is not selected.
• Random number tables are generated to ensure an equal chance of selection of every single unit in the population.
• They are accessible either in an issued form or can be generated by employing relevant software packages.
• In this method, units of the population don’t have equal chances of being selected. 
• The convenience or interpretation of the investigator plays a crucial role in the adoption of the sample. 
• They are chiefly selected based on belief, purpose, ease, or quota and are non-random samples.

Sampling and Non-sampling Errors

While conducting surveys, in class 11 collection, organisation and presentation of data, sample and non-sampling errors find an important mention. 

• Sampling error applies to the variations between the sample estimate and the actual value.
• It is the error that transpires when you observe the sample taken from the population. 
• The point of differentiation between the actual parameter of the population and its estimate is known as sampling error. 

Non-sampling errors are more consequential than sampling errors. Sampling error can be minimized by taking a larger sample, on the other hand, it is difficult to minimize non-sampling error. Even a Census can carry non-sampling errors.

 Some of the non-sampling errors are:

• Errors in Data Acquisition: This type of error stems from recording inaccurate responses.
• Non-Response Errors: Non-response happens if an interviewer is incapable to contact a person listed in the sample or a person from the sample declined to respond. In this case, the sample research may not be representative.
• Sampling Bias: Sampling bias happens when the sampling plan is such that some portion of the target population could not possibly be incorporated into the sample.

Must Read: Class 11 Oscillations Notes

The census of India is a very important body of our country and is an important part in the chapter class 11 collection, organisation and presentation of data. 

• The Census of India and the National Sample Survey Organisation (NSSO), are two significant firms at the national level, which gather, manner, and tabulate data.
• The Census of India produces the most comprehensive and continuous demographic record of the population. 
• The NSSO was established by the Government of India to conduct nationwide surveys on socio-economic issues. 
• NSSO gives periodic measures of education, school enrolment, utilization of educational aids, employment, unemployment, manufacturing, and service sector enterprises, morbidity, maternity, child care, utilization of the public distribution system, etc.

Ans. Three methods exist for gathering data: Personal meetings. Telephonic Interviews, and mailing surveys with questions.

Ans. The term “presentation of data” refers to the display of data in a way that makes it easy for viewers to understand and examine it.

Ans. Based on the methods used to acquire them, data can be divided into four basic categories: observational, experimental, simulational, and generated. The kind of research data you gather may have an impact on how you manage that data.

Also Read: Class 11 Formation of a Company

We hope the Class 11- Collection of Data notes helped you understand the essential concepts covered in this chapter. Still unsure about which stream to choose after Class 12. Our Leverage Edu experts are here to guide you in selecting the right stream of study to make sure that you make an informed decision. Sign up for a free session with us now!

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Presentation of Data Class 11 Statistics Notes And Questions

Please refer to Presentation of Data Class 11 Statistics notes and questions with solutions below. These Class 11 Statistics revision notes and important examination questions have been prepared based on the latest Statistics books for Class 11. You can go through the questions and solutions below which will help you to get better marks in your examinations.

Class 11 Statistics Presentation of Data Notes and Questions

The presentation of data means exhibition of the data in such a dear and attractive manner that these are easily understood and analysed. There are many forms of presentation of data of which the following three are well known: (i) Textual or Descriptive Presentation, (ii) Tabular Presentation, and (iii) Diagrammatic Presentation. The present chapter focuses on Textual and Tabular Presentation of data. Diagrammatic Presentation of data is discussed in the next chapter.

1. TEXTUAL PRESENTATION In textual presentation, data are a part of the text of study or a part of the description of the subject matter of study. Such a presentation is also called descriptive presentation of data. This is the most common form of data presentation when the quantity of data is not very large. Here are some examples:

Example 1 In a strike call given by the trade unions of shoe making industry in the city of Delhi, 50% of the workers reported for the duty, and only 2 out of the 20 industries in the city were totally closed.

Example 2 Surveys conducted by a Non-government Organisation reveal that, in the state of Punjab, area under pulses has tended to shrink by 40% while the area under rice and wheat has tended to expand by 20%, between the years 2001-2011.

Suitability Textual presentation of data is most suitable when the quantum of data is not very large. A small volume of data presented as a part of the subject matter of study becomes a useful supportive evidence to the text. Thus, rather than saying that price of gold is skyrocketing, a statement like price of gold has risen by 50% during the financial year 2017- 18 is much more meaningful and precise. One need not support the text with voluminous data in the form of tables or diagram when the textual matter itself is very small and includes only a few observations. Indeed, textual presentation of data is an integral component of a small quantitative description of a phenomenon. It gives an emphasis of statistical truth to the otherwise qualitative observations.

Drawbacks A serious drawback of die textual presentation of data is that one has to go through the entire text before quantitative facts about a phenomenon become evident. A picture or a set of bars showing increase in the price of gold during a specified period is certainly quite informative even on a casual glance of the reader. Textual presentation of data, on the other hand, does not offer anything to the reader at a mere glance of the text matter. The reader must read and comprehend (he entire text. When the subject under study is vast and involves comparison across different areas/countries, textual presentation of data would only add to discomfort of the reader.

2. TABULAR PRESENTATION In the words of Neiswanger, “A statistical table is a systematic organisation of data in columns and rows” Vertical dissections of table (||) are known as columns and horizontal dissections (=) are known as rows.

Tabulation is the process of presenting data in the form of a table. According to Prof. L.R. Connor, ‘tabulation involves the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration. ”

In the words of Prof. M.M. Blair, “Tabulation in its broadest sense is an orderly arrangement of data in columns and rows.”

Components of a Table Following are the principal components of a table:

(1) Table Number: First of all, a table must be numbered. Different tables must have different numbers, e.g., 1, 2, 3, etc. These numbers must be in the same order as the tables. Numbers facilitate location of the tables.

(2) Title: A table must have a title. Title must be written in bold letters. It should attract the attention of the readers. The title must be simple, clear and short. A good title must reveal: (i) the problem under consideration, (ii) the time period of the study, (iii) the place of study, and (iv) the nature of classification of data. A good title is short but complete in all respects.

(3) Head Note: If the title of the table does not give complete information, it is supplemented with a head note. Head note completes the information in the title of the table. Thus, units of the data are generally expressed in the form of lakhs, tonnes, etc. and preferably in brackets as a head-note.

(4) Stubs: Stubs are titles of the rows of a table. These titles indicate information contained in the rows of the table.

(5) Caption: Caption is the title given to the columns of a table. A caption indicates information contained in the columns of the table. A caption may have sub-heads when information contained in the columns is divided in more than one class. For example, a caption of ‘Students’ may have boys and girls as sub-heads.

(6) Body or Field: Body of a table means sum total of the items in the table. Thus, body is the most important part of a table. It indicates values of the various items in the table. Each item in the body is called ‘cell’.

(7) Footnotes: Footnotes are given for clarification of the reader. These are generally given when information in the table need to be supplemented. «

(8) Source: When tables are based on secondary data, source of the data is to be given. Source of the data is specified below the footnote. It should give: name of the publication and publisher, year of publication, reference, page number, etc.

Difference between Table and Tabulation

While tabulation refers to the method or process of presenting data in the form of rows and columns, table refers to the actual presentation of data in the form of rows and columns. Table is the consequence (result) of tabulation.

Check [he following format of a table showing its various components:

Guidelines for the Construction of a Table or Features of a Good Table

Construction of a table depends upon the objective of study. It also depends upon the wisdom of the statistician. There are no hard and fast rules for the construction of a table. However, some important guidelines should be kept in mind. These guidelines are features of a good table. These are as under:

(1) Compatible Title: Title of a table must be compatible with the objective of the study. The title should be placed at the top centre of the table.

(2) Comparison: It should be kept in mind that items (cells) which are to be compared with each other are placed in columns or rows close to each other. This facilitates comparison.

(3) Special Emphasis: Some items in the table may need special emphasis. Such items should be placed in the head rows (top above) or head columns (extreme left). Moreover, such items should be presented in bold figures.

(4) Ideal Size: Table must be of an ideal size. To determine an ideal size of a table, a rough draft or sketch must be drawn. Rough draft will give an idea as to how many rows and columns should be drawn for presentation of the data.

(5) Stubs: If rows are very long, stubs may be given at the right hand side of the table also.

(6) Use of Zero: Zero should be used only to indicate the quantity of a variable. It should not be used to indicate the non-availability of data. If the data are not available, it should be indicated by ‘n.a.’ or (-) hyphen sign.

(7) Headings: Headings should generally be written in the singular form. For example, in the columns indicating goods, the word ‘good’ should be used.

(8) Abbreviations: Use of abbreviations should be avoided in the headings or subheadings of the table. Short forms of the words such as Govt., m.p. (monetary policy), etc. should not be used. Also such signs as “(ditto)” should not be used in the body of the table.

(9) Footnote: Footnote should be given only if needed. However, if footnote is to be given, it must bear some asterisk mark (*) corresponding to the concerned item. (10) Units: Units used must be specified above the columns. If figures are very large, units may be noted in the short form as ‘000’ hectare or ‘000’ tonnes.

(11) Total: In the table, sub-totals of the items must be given at the end of each row. Grand total of the items must also be noted.

(12) Percentage and Ratio: Percentage figures should be provided in the table, if possible. This makes the data more informative.

(13) Extent of Approximation: If some approximate figures have been used in the table, the extent of approximation must be noted. This may be indicated at the top of the table as a part of head note or at the foot of the table as a footnote.

(14) Source of Data: Source of data must be noted at the foot of the table. It is generally noted next to the footnote.

(15) Size of Columns: Size of the columns must be uniform and symmetrical.

(16) Ruling of Columns: Columns may be divided into different sections according to similarities of the data.

(17) Simple, Economical and Attractive: A table must be simple, attractive and economical in space.

Kinds of Tables There are three basis of classifying tables, viz., (1) purpose of a table, (2) originality of a table, and (3) construction of a table. According to each of these bases, statisticians have classified tables as in the following flow chart:

Let us attempt a brief description of the various kinds of tables:

(1) Tables according to Purpose

According to purpose, there are two kinds of tables:

(i) General Purpose Table: General purpose table is that table which is of general use. It does not serve any specific purpose or specific problem under consideration. Such tables are just ‘data bank’ for the use of researchers for their various studies. These tables are generally attached to some official reports, like Census Reports oflndia. These are also called Reference Tables.

(ii) Special Purpose Table: Special purpose table is that table which is prepared with some specific purpose in mind. Generally, these are small tables limited to the problem under consideration. In these tables data are presented in the form of result of the analysis. That is why these tables are also called summary tables.

(2) Tables according to Originality On the basis of originality, tables are of two kinds: (i) Original Table: An original table is that in which data are presented in the same form and manner in which they are collected. (ii) Derived Table: A derived table is that in which data are not presented in the form or manner in which these are collected. Instead the data are first converted into ratios or percentage and then presented.

(3) Tables according to Construction

According to construction, tables are of two kinds:

(i) Simple or One-way Table: A simple table is that which shows only one characteristic of the data. Table 2 below is an example of a simple table. It shows number of students in a college:

(ii) Complex Table: A complex table is one which shows more than one characteristic of the data. On the basis of the characteristics shown, these tables may be further classified as:

(a) Double or Two-way Table: A two-way table is that which shows two characteristics of the data. For example, Table 3, showing the number of students in different classes according to their sex, is a two-way table:                          Number of Students in a College                            (According to Sex and Class)

(b) Treble Table: A treble table is that which shows three characteristics of the data. For example, Table 4 shows number of students in a college according to class, sex and habitation.                                       Number of Students in a College                                   (According to Class, Sex and Habitation)

(c) Manifold Table: A manifold table is the one which shows more than three characteristics of the data. Table 5, for example, shows number of students in a college according to their sex, class, habitation and marital status.                                   Number of Students in a College                      (According to their Sex, Class, Habitation and Marital Status)

Classification of Data and Tabular Presentation Tabular presentation is based on four-fold classification of data, viz., qualitative, quantitative, temporal, and spatial. Following are the details with suitable illustrations.

(1) Qualitative Classification of Data and Tabular Presentation: Qualitative classification occurs when data are classified on the basis of qualitative attributes or qualitative characteristics of a phenomenon. Example: Data of unemployment may relate to rural-urban areas, skilled and unskilled workers, or male and female job-seekers. Table 6 below is an example of tabular presentation of data when data are classified on the basis of qualitative attributes or qualitative characteristics.

(This is an imaginary table. In this table, male and female are such characteristics/attributes which are qualitative and cannot be quantified.)

(2) Quantitative Classification of Data and Tabular Presentation: Quantitative classification occurs when data are classified on the basis of quantitative characteristics of a phenomenon.

Example: Data on marks in Mathematics by the students of Class XII in CBSE examination. Table 7 shows tabular presentation of data when data are classified on the basis of quantitative characteristics.

Marks Obtained by Students of Class XII of XYZ School

Source: Result Sheets Here, marks are a quantifiable variable and data are classified in terms of different class intervals of marks.

(3) Temporal Classification of Data and Tabular Presentation:

In temporal classification, data are classified according to time, and time becomes the classifying variable.

Example: Sale of Cell phones in different years during the period 2014-2018 in the city of Delhi. Table 8 shows tabular presentation of data on the basis of temporal classification.

Annual Sale of Cell Phones in the City of Delhi (2014-2018)

(4) Spatial Classification : In spatial classification, place/location becomes the classifying variable. It may be a village, a town, a district, a state or a country as a whole. Example: Number of Indian students studying in different countries of the world during a particular year. Table 9 is an example of tabular presentation based on spatial classification of data.

Indian Students in different Countries of the World (2018)

Merits of Tabular Presentation Following are the principal merits of tabular presentation of data:

(1) Simple and Brief Presentation: Tabular presentation is perhaps the most simplest form of data presentation. Data, therefore, are easily understood. Also, a large volume of statistical data is presented in a very brief form.

(2) Facilitates Comparison: The tabulation facilitates comparison of data by presenting the data in different classes.

(3) Easy Analysis: It is very easy to analyse the data from tables. It is by organising the data in the form of table that one finds out their central tendency, dispersion and correlation.

(4) Highlights Characteristics of Data: Tabulation highlights characteristics of data. Accordingly, it becomes easy to remember the statistical facts.

(5) Economical: Tabular presentation is a very economical mode of data presentation. It saves time as well as space.

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• Diagrammatic Presentation of Data

Nowadays a lot of emphases is laid upon exceptional presentation of data.  All of this is because, when presented diagrammatically, data is easy to interpret with just a glance. In such a case we need to learn how to represent data diagrammatically via bar diagrams, pie charts etc.

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Bar diagrams.

As the name suggests, when data is presented in form of bars or rectangles , it is termed to be a bar diagram.

Features of a Bar

• The rectangular box in a bar diagram is known as a bar. It represents the value of a variable .
• These bars can be either vertically or horizontally arranged.
• Bars are equidistant from each other.
• Each bar originates from a common baseline or a common axis.
• The width of bars remain same but the height changes, according to the value of a variable, to denote the difference between their values.
• Unless they are in a specific order, the convention is that bars can be arranged in an ascending or descending order.

Browse more Topics under Presentation Of Data

• Textual and Tabular Presentation of Data

Types of Bar Diagrams

Simple bar diagram.

These are the most basic type of bar diagrams. A simple bar diagram represents only a single set of numerical data. Generally, simple bar diagrams are used to represent time series data for a single entity.

Generally, the Y-axis contains markings which represent the range of the value of variable whereas the X-axis contains divisions for entities like years, time periods, areas etc.

Multiple Bar Diagram

Unlike single bar diagram, a multiple bar diagram can represent two or more sets of numerical data on the same bar diagram. Generally, these are constructed to facilitate comparison between two entities like average height and average weight, birth rates and death rates etc.

Separate sets of numerical data are differentiated with the help of colour variation. By the same token of simple bar diagrams, multiple bar diagrams also have divisions on Y-axis and X-axis that represent different values of the variable and entities like year, areas etc. respectively. Note that each division on X-axis has two or more bar diagrams each according to the specified number of bars.

Sub-divided or Differential Bar Diagrams

Sub-divided bar diagrams are useful when we need to represent the total values and the contribution of various sections of the total simultaneously. The different sections are shaded with different colours in the same bar.

For example, such a bar diagram can be used to represent the varying levels of employment over the years in India and each bar can be divided into two sectors, the urban and rural. Again, here the Y-axis and X-axis represent same values as in simple and multiple bar diagrams.

Percentage Bar Diagrams

This is derived further from the subdivided bar diagrams. In this, each bar has the same height that represents 100 percent of the Y-axis in totality. Further, each bar is divided into sections based on percentages calculated according to the contribution of these sections.

Percentage bar diagrams are used when the values are really high. This is because using subdivided bar diagrams in such cases would not be easy and appropriate.

Deviation Bar Diagrams

Lastly, the deviation bar diagrams are most interesting of the lot. In such a type of bar diagram, there are both negative and positive values on the y-axis. The deviation bar diagrams are used to compare the net deviation of related variables with respect to time and location.

For example, it can be used to represent a bar diagram for savings (represented by positive deviations) and deficit (represented by negative deviations) over years.

Pie or Circular Diagrams

In addition to bar diagrams, pie diagrams are also widely used to pictorially represent data. In this, a circle is divided into various segments which are decided on the basis of percentages. Which means the circle is divided into sectors depending on various percentages.

These sectors are differentiated with the help of colours. Pie diagrams have an edge over bar diagrams because they can easily provide an overview and provides a better sense of contributions of each part. The steps for construction of a pie diagram are:

The first step involves finding out respective percentages. This is done by a simple mathematical formula to find out percentages which is –

{(Parts for the respective sector)/total parts) ×100} .

For example, if in a class of 1oo students, 30 are obese, 20 are fat and 50 are slim then the percentages will be as follows:

(30/100) × 100= 30%

(20/100) × 100= 20%

(50/100) × 100= 50%

2] A circle comprises 360 degrees. The angles that each sector will span across is decided by the given formula: (Percentage value/100)×360°

3] Finally, just plot these values according to their respective angles on a circle and give appropriate markings to complete the pie chart.

A Solved Example for You

Q:   Which among the following is not a feature of a bar in the bar diagram?

• The width is same but the heights are generally different
• They are rectangular in shape
• Bars should not be equidistant
• Each bar originates from a common baseline

Ans:   Of all the above options, option C is incorrect because conventionally the bars should be equidistant.

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Presentation of Data

• Textual And Tabular Presentation Of Data

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Present Your Data Like a Pro

• Joel Schwartzberg

Demystify the numbers. Your audience will thank you.

While a good presentation has data, data alone doesn’t guarantee a good presentation. It’s all about how that data is presented. The quickest way to confuse your audience is by sharing too many details at once. The only data points you should share are those that significantly support your point — and ideally, one point per chart. To avoid the debacle of sheepishly translating hard-to-see numbers and labels, rehearse your presentation with colleagues sitting as far away as the actual audience would. While you’ve been working with the same chart for weeks or months, your audience will be exposed to it for mere seconds. Give them the best chance of comprehending your data by using simple, clear, and complete language to identify X and Y axes, pie pieces, bars, and other diagrammatic elements. Try to avoid abbreviations that aren’t obvious, and don’t assume labeled components on one slide will be remembered on subsequent slides. Every valuable chart or pie graph has an “Aha!” zone — a number or range of data that reveals something crucial to your point. Make sure you visually highlight the “Aha!” zone, reinforcing the moment by explaining it to your audience.

With so many ways to spin and distort information these days, a presentation needs to do more than simply share great ideas — it needs to support those ideas with credible data. That’s true whether you’re an executive pitching new business clients, a vendor selling her services, or a CEO making a case for change.

• JS Joel Schwartzberg oversees executive communications for a major national nonprofit, is a professional presentation coach, and is the author of Get to the Point! Sharpen Your Message and Make Your Words Matter and The Language of Leadership: How to Engage and Inspire Your Team . You can find him on LinkedIn and X. TheJoelTruth

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• Qualitative data
• Quantitative data
• Summarising data using graphs
• Graphs presented in misleading ways
• Summarising data numerically
• Distribution

Data presentation

Data can be binary, nominal, ordered, discrete quantitative, or continuous quantitative.

Graphs include bar-charts, pie-charts, histograms, box-and-whisker plots and scatter diagrams. The type of graph used should be chosen according to the type of data being displayed. Be aware that graphs may be presented in misleading ways. Furthermore, graphs can be symmetrical, positively skewed or negatively skewed.

Types of average include the mean, median, and mode. Measures of spread include the range, interquartile range, variance, and standard deviation. Means and measures of spread should be chosen according to the type of data being summarised and some measures are susceptible to outliers.

Qualitative data may be binary , nominal , or ordered .

Qualitative variables have no numerical significance (e.g. we cannot add up or multiply together any values that are assigned to the categories). Qualitative data can be binary, nominal or ordered.

Binary variables, such as whether or not someone arriving at an A&E department is admitted to a ward, have only two categories.

Nominal variables have several categories (e.g. type of scan: CT, MRI, or PET). Any figures attached to the categories (such as CT = 1, MRI = 2, PET = 3) have no numerical meaning.

Ordered (or ordinal) variables also have several categories but these can be ranked or ordered using numbers (e.g. health: very poor = 1, poor = 2, intermediate = 3, good = 4, very good = 5).

An individual categorised as having good health is less well than one whose health is rated as very good, but is in better health than someone who has a health rating of intermediate. Note that differences between categories (such as 4 - 3 or 3 – 2 in the example above) do not have a meaningful numerical interpretation.

Quantitative data can be counted or measured .

Quantitative variables take measured values, which may be further divided into discrete or continuous variables.

Those consisting of whole numbers only are described as discrete quantitative.

An example is the number of visits that a patient makes to an outpatient clinic during a calendar year.

Quantitative variables may be continuous and can take values that are constrained only by the accuracy of measurement.

For instance, blood glucose level is usually stated in mmol/L to one decimal place with a normal individual typically having a value of approximately 5.5. Differences between quantitative values are numerically meaningful; two patients differ between themselves by precisely one outpatient visit per year whether their values are 2 and 1 or 12 and 11 (say).

Graphs display data and should be chosen according to the type of data being presented .

Commonly used graphs include bar- and pie-charts, histograms, box-and-whisker plots and scatter diagrams. Graphs can be symmetrical, positively skewed or negatively skewed. Be aware that graphs may be presented in misleading ways.

A bar-chart can be used for nominal data, ordered data or, if there are only a few categories, whole numbers.

The bars should be spaced apart, with each height being proportional to the category’s percentage out of the total number of observations.

Pie-charts operate in a similar manner but use sectors within a circle; the angle of each sector is proportional to the category’s percentage out of the total number of observations.

With quantitative data, histograms should be used rather than bar-charts. Bars should not have gaps between them as each represents an interval for the variable under consideration.

The histogram is constructed using the number of observations in each interval. It is good practice to use intervals of equal width, as the height of each bar is then proportional to the category’s percentage out of the total number of observations.

The number of intervals to be used should be considered carefully. Too few intervals may prevent important features of the distribution from being identified, whereas too many lead to a distribution with a jagged rather than a smooth shape.

In practice, the number of intervals that should be used is constrained by the size of the sample; a common guideline is that the number of intervals (x) should be roughly equal to the square root (√) of the sample size (n) (e.g. x = √n). Given that a histogram needs at least five bars to be helpful, it is recommended that there should be a minimum of 30 observations.

Box-and-whisker plot

An alternative type of graph suitable for continuous quantitative data is the box-and-whisker plot. Values are plotted against the vertical axis.

The main features of a box-and-whisker diagram are based around a line that is parallel to the vertical axis of the graph. Around the centre of the plot there is a rectangle that is divided into two by a horizontal line. This middle line corresponds to the median value of the variable, with the upper and lower horizontal sides of the rectangle representing the upper and lower quartiles of the distribution respectively (these three quantities are defined below).

Vertical whiskers extend from the horizontal edges of the rectangle in both directions; these represent the range of other non-extreme values. Any extreme values, known as outliers, are shown as small circles beyond the limits of the whiskers. Unfortunately, there is no convention as to what constitutes an outlier so a subjective decision may be required.

Comparing groups

The methods described above can be extended to contrast two or more groups within a sample. For example, the size of mechanical valves implanted in heart surgery can be compared for male and female patients by constructing two bar-charts.

If two continuous variables are being compared, such as height and weight, a scatter diagram can be drawn using a two-dimensional plot.

Scatter diagram

During child development, weight becomes greater with increasing height. Weight is therefore referred to as the outcome variable, with height being the explanatory variable. In a scatter diagram, the outcome variable (weight) is on the vertical axis and the explanatory variable (height) is on the horizontal axis.

Each member of the sample (each child in a group of young people) can be marked on the scatter diagram with a plotted symbol located using that individual’s height and weight values.

Trends over time can be illustrated as line plots. For instance, the number of cases of measles in the UK for consecutive years can be shown as points with the numbers represented by the vertical axis, the base set at zero, and the years indicated along the horizontal axis. Adjacent points are joined together by straight lines to highlight trends.

It is common to encounter graphs that have been drawn in misleading ways .

For instance, in a graph of trends over time the base of the vertical axis may correspond to a non-zero number in order to give a magnified impression of the size of any changes.

Avoid plotting mean values of groups as bar-charts; this is inappropriate as these charts have been designed for percentages and numbers of observations. In the medical literature, a handle is often attached to the top of each bar in order to give an indication of the variation of the observations within each group, although the way in which the variation has been measured is often not explained.

Using a ploy similar to the non-zero origin that can be found in time trend graphs, bar-charts may be presented with a broken vertical axis. This effectively removes a middle section of the axis in order to inflate differences between the bar heights.

In the media, pie-charts are often given a three-dimensional representation, which is thought to be more eye catching than the traditional circle. However, this method of presentation can create an optical illusion whereby the sectors in the lower region of the resulting ellipse appear magnified and those in the upper region appear contracted.

It is important not only to illustrate data graphically but also to summarise the main features using straightforward arithmetic.

An impression of the size of a typical value from a distribution may be found by calculating an average. There are three main types:

The mean is obtained by summing the values. This total is then divided by the size of the sample.

The median is the middle observation when the values are ordered in terms of size. If the number of observations is even, the mean of the middle pair is calculated.

The mode is found from a frequency count of the values recorded and is the most common value.

Variability

The variability of the observations is summarised using a measure of spread. Methods include the range, the interquartile range, the variance, and the standard deviation.

Range & interquartile range

The range is the difference between the largest and smallest values. The interquartile range is the difference between the upper and lower quartiles, where the upper quartile is the value midway between the median and the largest value and the lower quartile is midway between the smallest value and the median.

The variance is found by subtracting the mean from each observation, squaring each of these differences, summing them, and dividing the total by the sample size minus one.

Standard deviation

The standard deviation is calculated as the square root of the variance. Standard deviations are generally preferred to variances as they are in the same units as those of the original observations (for instance, if systolic blood pressure is measured in mm Hg, the standard deviation values will be in mm Hg).

Outliers can have a considerable impact on some types of average and measures of spread.

The mean can be inflated by a single extremely large value, along with the variance and standard deviation. The median and interquartile range are only influenced by outliers if they form a substantial fraction of the whole sample.

By definition, the range is highly susceptible to outliers and it tends to increase as the sample size becomes larger.

The shape of distribution should be checked in terms of the values away from the central region (or the tails of the distribution).

For this introductory discussion it is assumed that the distribution has only one peak. Variables can be symmetrical (as with adult weight in some populations), positively skewed having a few extremely high values and a long tail pointing in the positive direction (e.g. adult alcohol consumption) or negatively skewed by a few extremely low values with a long tail pointing in the negative direction (e.g. length of gestation for live births).

There is an important relationship between the mean, median and the presence or absence of symmetry. For symmetrical distributions the mean and the median are equal. Positively skewed distributions have a mean greater than the median, and negatively skewed distributions have a median greater than the mean.

Other distributions that are encountered include those with more than one peak (e.g. the blood glucose measurements in mmol/L for a mixed group of normal and diabetic individuals) and U-shaped distributions for which observations are less likely to occur in the central portion of the distribution than towards the edges.

Last updated: January 2023

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Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

• Accountancy
• Business Studies
• Organisational Behaviour
• Human Resource Management
• Entrepreneurship
• CBSE Class 11 Statistics for Economics Notes

Chapter 1: Concept of Economics and Significance of Statistics in Economics

• Statistics for Economics | Functions, Importance, and Limitations

Chapter 2: Collection of Data

• Methods of Data Collection
• Sources of Data Collection | Primary and Secondary Sources
• Direct Personal Investigation: Meaning, Suitability, Merits, Demerits and Precautions
• Indirect Oral Investigation : Suitability, Merits, Demerits and Precautions
• Difference between Direct Personal Investigation and Indirect Oral Investigation
• Information from Local Source or Correspondents: Meaning, Suitability, Merits, and Demerits
• Questionnaires and Schedules Method of Data Collection
• Difference between Questionnaire and Schedule
• Qualities of a Good Questionnaire and Types of Questionnaires
• What are the Published Sources of Collecting Secondary Data?
• What Precautions should be taken before using Secondary Data?
• Two Important Sources of Secondary Data: Census of India and Reports & Publications of NSSO
• What is National Sample Survey Organisation (NSSO)?
• What is Census Method of Collecting Data?
• Sample Method of Collection of Data
• Methods of Sampling
• Father of Indian Census
• What makes a Sampling Data Reliable?
• Difference between Census Method and Sampling Method of Collecting Data
• What are Statistical Errors?

Chapter 3: Organisation of Data

• Organization of Data
• Objectives and Characteristics of Classification of Data
• Classification of Data in Statistics | Meaning and Basis of Classification of Data
• Concept of Variable and Raw Data
• Types of Statistical Series
• Difference between Frequency Array and Frequency Distribution
• Types of Frequency Distribution

Chapter 4: Presentation of Data: Textual and Tabular

• Textual Presentation of Data: Meaning, Suitability, and Drawbacks

Tabular Presentation of Data: Meaning, Objectives, Features and Merits

• Different Types of Tables
• Classification and Tabulation of Data

Chapter 5: Diagrammatic Presentation of Data

• Diagrammatic Presentation of Data: Meaning , Features, Guidelines, Advantages and Disadvantages
• Types of Diagrams
• Bar Graph | Meaning, Types, and Examples
• Pie Diagrams | Meaning, Example and Steps to Construct
• Histogram | Meaning, Example, Types and Steps to Draw
• Frequency Polygon | Meaning, Steps to Draw and Examples
• Ogive (Cumulative Frequency Curve) and its Types
• What is Arithmetic Line-Graph or Time-Series Graph?
• Diagrammatic and Graphic Presentation of Data

Chapter 6: Measures of Central Tendency: Arithmetic Mean

• Measures of Central Tendency in Statistics
• Arithmetic Mean: Meaning, Example, Types, Merits, and Demerits
• What is Simple Arithmetic Mean?
• Calculation of Mean in Individual Series | Formula of Mean
• Calculation of Mean in Discrete Series | Formula of Mean
• Calculation of Mean in Continuous Series | Formula of Mean
• Calculation of Arithmetic Mean in Special Cases
• Weighted Arithmetic Mean

Chapter 7: Measures of Central Tendency: Median and Mode

• Median(Measures of Central Tendency): Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Median for Different Types of Statistical Series
• Calculation of Median in Individual Series | Formula of Median
• Calculation of Median in Discrete Series | Formula of Median
• Calculation of Median in Continuous Series | Formula of Median
• Graphical determination of Median
• Mode: Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Mode in Individual Series | Formula of Mode
• Calculation of Mode in Discrete Series | Formula of Mode
• Grouping Method of Calculating Mode in Discrete Series | Formula of Mode
• Calculation of Mode in Continuous Series | Formula of Mode
• Calculation of Mode in Special Cases
• Calculation of Mode by Graphical Method
• Mean, Median and Mode| Comparison, Relationship and Calculation

Chapter 8: Measures of Dispersion

• Measures of Dispersion | Meaning, Absolute and Relative Measures of Dispersion
• Range | Meaning, Coefficient of Range, Merits and Demerits, Calculation of Range
• Calculation of Range and Coefficient of Range
• Interquartile Range and Quartile Deviation
• Partition Value | Quartiles, Deciles and Percentiles
• Quartile Deviation and Coefficient of Quartile Deviation: Meaning, Formula, Calculation, and Examples
• Quartile Deviation in Discrete Series | Formula, Calculation and Examples
• Quartile Deviation in Continuous Series | Formula, Calculation and Examples
• Mean Deviation: Coefficient of Mean Deviation, Merits, and Demerits
• Calculation of Mean Deviation for different types of Statistical Series
• Mean Deviation from Mean | Individual, Discrete, and Continuous Series
• Mean Deviation from Median | Individual, Discrete, and Continuous Series
• Standard Deviation: Meaning, Coefficient of Standard Deviation, Merits, and Demerits
• Standard Deviation in Individual Series
• Standard Deviation in Discrete Series
• Standard Deviation in Frequency Distribution Series
• Combined Standard Deviation: Meaning, Formula, and Example
• How to calculate Variance?
• Coefficient of Variation: Meaning, Formula and Examples
• Lorenz Curveb : Meaning, Construction, and Application

Chapter 9: Correlation

• Correlation: Meaning, Significance, Types and Degree of Correlation
• Methods of Measurements of Correlation
• Scatter Diagram Correlation | Meaning, Interpretation, Example
• Spearman's Rank Correlation Coefficient in Statistics
• Karl Pearson's Coefficient of Correlation | Assumptions, Merits and Demerits
• Karl Pearson's Coefficient of Correlation | Methods and Examples

Chapter 10: Index Number

• Index Number | Meaning, Characteristics, Uses and Limitations
• Methods of Construction of Index Number
• Unweighted or Simple Index Numbers: Meaning and Methods
• Methods of calculating Weighted Index Numbers
• Fisher's Index Number as an Ideal Method
• Fisher's Method of calculating Weighted Index Number
• Paasche's Method of calculating Weighted Index Number
• Laspeyre's Method of calculating Weighted Index Number
• Laspeyre's, Paasche's, and Fisher's Methods of Calculating Index Number
• Consumer Price Index (CPI) or Cost of Living Index Number: Construction of Consumer Price Index|Difficulties and Uses of Consumer Price Index
• Methods of Constructing Consumer Price Index (CPI)
• Wholesale Price Index (WPI) | Meaning, Uses, Merits, and Demerits
• Index Number of Industrial Production : Characteristics, Construction & Example
• Inflation and Index Number

Important Formulas in Statistics for Economics

• Important Formulas in Statistics for Economics | Class 11

What is Tabulation?

The systematic presentation of numerical data in rows and columns is known as Tabulation . It is designed to make presentation simpler and analysis easier. This type of presentation facilitates comparison by putting relevant information close to one another, and it helps in further statistical analysis and interpretation. One of the most important devices for presenting the data in a condensed and readily comprehensible form is tabulation. It aims to provide as much information as possible in the minimum possible space while maintaining the quality and usefulness of the data.

“Tabulation involves the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration.” – L.R. Connor

Objectives of Tabulation

The aim of tabulation is to summarise a large amount of numerical information into the simplest form. The following are the main objectives of tabulation:

• To make complex data simpler: The main aim of tabulation is to present the classified data in a systematic way. The purpose is to condense the bulk of information (data) under investigation into a simple and meaningful form.
• To save space: Tabulation tries to save space by condensing data in a meaningful form while maintaining the quality and quantity of the data.
• To facilitate comparison: It also aims to facilitate quick comparison of various observations by providing the data in a tabular form.
• To facilitate statistical analysis: Tabulation aims to facilitate statistical analysis because it is the stage between data classification and data presentation. Various statistical measures, including averages, dispersion, correlation, and others, are easily calculated from data that has been systematically tabulated.
• To provide a reference: Since data may be easily identifiable and used when organised in tables with titles and table numbers, tabulation aims to provide a reference for future studies.

Features of a Good Table

Tabulation is a very specialised job. It requires a thorough knowledge of statistical methods, as well as abilities, experience, and common sense. A good table must have the following characteristics:

• Title: The top of the table must have a title and it needs to be very appealing and attractive.
• Manageable Size: The table shouldn’t be too big or too small. The size of the table should be in accordance with its objectives and the characteristics of the data. It should completely cover all significant characteristics of data.
• Attractive: A table should have an appealing appearance that appeals to both the sight and the mind so that the reader can grasp it easily without any strain.
• Special Emphasis: The data to be compared should be placed in the left-hand corner of columns, with their titles in bold letters.
• Fit with the Objective: The table should reflect the objective of the statistical investigation.
• Simplicity: To make the table easily understandable, it should be simple and compact.
• Data Comparison: The data to be compared must be placed closely in the columns.
• Numbered Columns and Rows: When there are several rows and columns in a table, they must be numbered for reference.
• Clarity: A table should be prepared so that even a layman may make conclusions from it. The table should contain all necessary information and it must be self-explanatory.
• Units: The unit designations should be written on the top of the table, below the title. For example, Height in cm, Weight in kg, Price in ₹, etc. However, if different items have different units, then they should be mentioned in the respective rows and columns.
• Suitably Approximated: If the figures are large, then they should be rounded or approximated.
• Scientifically Prepared: The preparation of the table should be done in a systematic and logical manner and should be free from any kind of ambiguity and overlapping. 

Components of a Table

A table’s preparation is an art that requires skilled data handling. It’s crucial to understand the components of a good statistical table before constructing one. A table is created when all of these components are put together in a systematic order. In simple terms, a good table should include the following components:

1. Table Number:

Each table needs to have a number so it may be quickly identified and used as a reference.

• If there are many tables, they should be numbered in a logical order.
• The table number can be given at the top of the table or the beginning of the table title.
• The table is also identified by its location using subscripted numbers like 1.2, 2.1, etc. For instance, Table Number 3.1 should be seen as the first table of the third chapter.

Each table should have a suitable title. A table’s contents are briefly described in the title.

• The title should be simple, self-explanatory, and free from ambiguity.
• A title should be brief and presented clearly, usually below the table number.
• In certain cases, a long title is preferable for clarification. In these cases, a ‘Catch Title’ may be placed above the ‘Main Title’. For instance , the table’s contents might come after the firm’s name, which appears as a catch title.
• Contents of Title: The title should include the following information:  (i) Nature of data, or classification criteria (ii) Subject-matter (iii) Place to which the data relates  (iv) Time to which the data relates  (v) Source to which the data belongs  (vi) Reference to the data, if available.

3. Captions or Column Headings:

A column designation is given to explain the figures in the column at the top of each column in a table. This is referred to as a “Column heading” or “Caption”.

• Captions are used to describe the names or heads of vertical columns.
• To save space, captions are generally placed in small letters in the middle of the columns.

4. Stubs or Row Headings:

Each row of the table needs to have a heading, similar to a caption or column heading. The headers of horizontal rows are referred to as stubs. A brief description of the row headers may also be provided at the table’s left-hand top.

5. Body of Table:

The table’s most crucial component is its body, which contains data (numerical information).

• The location of any one figure or data in the table is fixed and determined by the row and column of the table.
• The columns and rows in the main body’s arrangement of numerical data are arranged from top to bottom.
• The size and shape of the main body should be planned in accordance with the nature of the figures and the purpose of the study.
• As the body of the table summarises the facts and conclusions of the statistical investigation, it must be ensured that the table does not have irrelevant information.

6. Unit of Measurement:

If the unit of measurement of the figures in the table (real data) does not change throughout the table, it should always be provided along with the title.

• However, these units must be mentioned together with stubs or captions if rows or columns have different units.
• If there are large figures, they should be rounded up and the rounding method should be stated.

7. Head Notes:

If the main title does not convey enough information, a head note is included in small brackets in prominent words right below the main title.

• A head-note is included to convey any relevant information.
• For instance, the table frequently uses the units of measurement “in million rupees,” “in tonnes,” “in kilometres,” etc. Head notes are also known as Prefatory Notes .

8. Source Note:

A source note refers to the place where information was obtained.

• In the case of secondary data, a source note is provided.
• Name of the book, page number, table number, etc., from which the data were collected should all be included in the source. If there are multiple sources, each one must be listed in the source note.
• If a reader wants to refer to the original data, the source note enables him to locate the data. Usually, the source note appears at the bottom of the table. For example, the source note may be: ‘Census of India, 2011’.
• Importance: A source note is useful for three reasons: -> It provides credit to the source (person or group), who collected the data; -> It provides a reference to source material that may be more complete; -> It offers some insight into the reliability of the information and its source.

9. Footnotes:

The footnote is the last part of the table. The unique characteristic of the data content of the table that is not self-explanatory and has not previously been explained is mentioned in the footnote.

• Footnotes are used to provide additional information that is not provided by the heading, title, stubs, caption, etc.
• When there are many footnotes, they are numbered in order.
• Footnotes are identified by the symbols *, @, £, etc.
• In general, footnotes are used for the following reasons: (i) To highlight any exceptions to the data (ii)Any special circumstances affecting the data; and (iii)To clarify any information in the data.

Merits of Tabular Presentation of Data

The following are the merits of tabular presentation of data:

• Brief and Simple Presentation: Tabular presentation is possibly the simplest method of data presentation. As a result, information is simple to understand. A significant amount of statistical data is also presented in a very brief manner.
• Facilitates Comparison: By grouping the data into different classes, tabulation facilitates data comparison.
• Simple Analysis: Analysing data from tables is quite simple. One can determine the data’s central tendency, dispersion, and correlation by organising the data as a table.
• Highlights Characteristics of the Data:  Tabulation highlights characteristics of the data. As a result of this, it is simple to remember the statistical facts.
• Cost-effective: Tabular presentation is a very cost-effective way to convey data. It saves time and space.
• Provides Reference: As the data provided in a tabular presentation can be used for other studies and research, it acts as a source of reference.

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Collection, Organisation and Presentation of Data Class 11 Notes (PDF) – आंकड़ों का संकलन संगठन एवं प्रस्तुतिकरण के नोट्स

Collection, Organisation and Presentation of Data Class 11 Notes ( कक्षा 11 अर्थशास्त्र आंकड़ों का संकलन संगठन एवं प्रस्तुतिकरण के नोट्स ) have been updated here for latest 11th syllabus. You can now download Collection, Organisation and Presentation of Data Notes PDF to study the complete chapter and revise it. This class 11 Economics notes contains summary and key points of the topic Collection, Organisation and Presentation of Data to help you quickly understand the chapter from 11th Economics textbook . And after reading the notes, you can use Class 11th Economics Solutions of Collection, Organisation and Presentation of Data to solve the questions.

Collection, Organisation and Presentation of Data Class 11 Notes

The Notes for class 11 Economics (अर्थशास्त्र) for the topic Collection, Organisation and Presentation of Data (आंकड़ों का संकलन संगठन एवं प्रस्तुतिकरण) is as follows.

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• Collection, Organisation and Presentation of Data
• Consumers Equilibrium and Demand
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• Forms Of Market and Price Determination
• Introduction to Index Numbers
• Introductory Microeconomics
• Measures of Central Tendency
• Measures of Dispersion
• Producer Behaviour and Supply
• Statistics for Economics

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The purpose of a scientific paper is to communicate, and within the paper this applies especially to the presentation of data.

Continuous data, such as serum cholesterol concentration or triceps skinfold thickness, can be summarised numerically either in the text or in tables or plotted in a graph. When numbers are given there is the problem of how precisely to specify them. As far as possible the numerical precision used should be consistent throughout a paper and especially within a table. In general, summary statistics such as means should not be given to more than one extra decimal place over the raw data. The same usually applies to measures of variability or uncertainty such as the standard deviation or standard error, though greater precision may be warranted for these quantities as they are often used in further calculations. Similar comments apply to the results of regression analyses, where spurious precision should be avoided. For example, the regression equation 1

birth weight=-3.0983527 + 0.142088xchest circumf + 0.158039 x midarm circumf, purports to predict birth weight to 1/1000000 g.

Categorical data, such as disease group or presence or absence of symptoms, can be summarised as frequencies and percentages. It can be confusing to give percentages alone, as the denominator may be unclear. Also, giving frequencies allows percentages to be given as integers, such as 22%, rather than more precisely. Percentages to one decimal place may sometimes be reasonable, but not in small samples; greater precision is unwarranted. Such data rarely need to be shown graphically.

Test statistics, such as values of t or χ 2 , and correlation coefficients should be given to no more than two decimal places. Confidence intervals are better presented as, say, “12.4 to 52.9” because the format “12.4-52.9” is confusing when one or both numbers are negative. P values should be given to one or two significant figures. P values are always greater than zero. Because computer output is often to a fixed number of decimal places P=0.0000 really means P<0.00005—such values should be converted to P<0.0001. P values always used to be quoted as P<0.05, P<0.01, and so on because results were compared with tabulated values of statistical distributions. Now that most P values are produced by computer they should be given more exactly, even for non-significant results—for example, P=0.2. Values such as P=0.0027 can be rounded up to P=0.003, but not in general to P<0.01 or P<0.05. In particular, the use of P<0.05 (or, even worse, P=NS) may conceal important information: there is minimal difference between P=0.06 and P=0.04. In tables, however, it may be necessary to use symbols to denote degrees of significance; a common system is to use *, **, and *** to mean P<0.05, 0.01, and 0.001 respectively. Mosteller gives a more extensive discussion of numerical presentation. 2

The choice between using a table or figure is not easy, nor is it easy to offer much general guidance. Tables are suitable for displaying information about a large number of variables at once, and graphs are good for showing multiple observations on individuals or groups, but between these cases lie a wide range of situations where the best format is not obvious. One point to consider when contemplating using a figure is the amount of numerical information contained. A figure that displays only two means with their standard errors or confidence intervals is a waste of space as a figure; either more information should be added, such as the raw data (a really useful feature of a figure), or the summary values should be put in the text.

In tables information about different variables or quantities is easier to assimilate if the columns (rather than the rows) contain like information, such as means or standard deviations. Interpretation of tables showing data for individuals (or perhaps for many groups) is aided by having the data ordered by one of the variables—for example, by the baseline value of the measurement of interest or by some important prognostic characteristic.

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Blog Data Visualization 10 Data Presentation Examples For Strategic Communication

10 Data Presentation Examples For Strategic Communication

Written by: Krystle Wong Sep 28, 2023

Knowing how to present data is like having a superpower. 

Data presentation today is no longer just about numbers on a screen; it’s storytelling with a purpose. It’s about captivating your audience, making complex stuff look simple and inspiring action. 

To help turn your data into stories that stick, influence decisions and make an impact, check out Venngage’s free chart maker or follow me on a tour into the world of data storytelling along with data presentation templates that work across different fields, from business boardrooms to the classroom and beyond. Keep scrolling to learn more! 

Click to jump ahead:

10 Essential data presentation examples + methods you should know

What should be included in a data presentation, what are some common mistakes to avoid when presenting data, faqs on data presentation examples, transform your message with impactful data storytelling.

Data presentation is a vital skill in today’s information-driven world. Whether you’re in business, academia, or simply want to convey information effectively, knowing the different ways of presenting data is crucial. For impactful data storytelling, consider these essential data presentation methods:

1. Bar graph

Ideal for comparing data across categories or showing trends over time.

Bar graphs, also known as bar charts are workhorses of data presentation. They’re like the Swiss Army knives of visualization methods because they can be used to compare data in different categories or display data changes over time. 

In a bar chart, categories are displayed on the x-axis and the corresponding values are represented by the height of the bars on the y-axis. 

It’s a straightforward and effective way to showcase raw data, making it a staple in business reports, academic presentations and beyond.

Make sure your bar charts are concise with easy-to-read labels. Whether your bars go up or sideways, keep it simple by not overloading with too many categories.

2. Line graph

Great for displaying trends and variations in data points over time or continuous variables.

Line charts or line graphs are your go-to when you want to visualize trends and variations in data sets over time.

One of the best quantitative data presentation examples, they work exceptionally well for showing continuous data, such as sales projections over the last couple of years or supply and demand fluctuations. 

The x-axis represents time or a continuous variable and the y-axis represents the data values. By connecting the data points with lines, you can easily spot trends and fluctuations.

A tip when presenting data with line charts is to minimize the lines and not make it too crowded. Highlight the big changes, put on some labels and give it a catchy title.

3. Pie chart

Useful for illustrating parts of a whole, such as percentages or proportions.

Pie charts are perfect for showing how a whole is divided into parts. They’re commonly used to represent percentages or proportions and are great for presenting survey results that involve demographic data. 

Each “slice” of the pie represents a portion of the whole and the size of each slice corresponds to its share of the total. 

While pie charts are handy for illustrating simple distributions, they can become confusing when dealing with too many categories or when the differences in proportions are subtle.

Don’t get too carried away with slices — label those slices with percentages or values so people know what’s what and consider using a legend for more categories.

4. Scatter plot

Effective for showing the relationship between two variables and identifying correlations.

Scatter plots are all about exploring relationships between two variables. They’re great for uncovering correlations, trends or patterns in data. 

In a scatter plot, every data point appears as a dot on the chart, with one variable marked on the horizontal x-axis and the other on the vertical y-axis.

By examining the scatter of points, you can discern the nature of the relationship between the variables, whether it’s positive, negative or no correlation at all.

If you’re using scatter plots to reveal relationships between two variables, be sure to add trendlines or regression analysis when appropriate to clarify patterns. Label data points selectively or provide tooltips for detailed information.

5. Histogram

Best for visualizing the distribution and frequency of a single variable.

Histograms are your choice when you want to understand the distribution and frequency of a single variable. 

They divide the data into “bins” or intervals and the height of each bar represents the frequency or count of data points falling into that interval. 

Histograms are excellent for helping to identify trends in data distributions, such as peaks, gaps or skewness.

Here’s something to take note of — ensure that your histogram bins are appropriately sized to capture meaningful data patterns. Using clear axis labels and titles can also help explain the distribution of the data effectively.

6. Stacked bar chart

Useful for showing how different components contribute to a whole over multiple categories.

Stacked bar charts are a handy choice when you want to illustrate how different components contribute to a whole across multiple categories. 

Each bar represents a category and the bars are divided into segments to show the contribution of various components within each category. 

This method is ideal for highlighting both the individual and collective significance of each component, making it a valuable tool for comparative analysis.

Stacked bar charts are like data sandwiches—label each layer so people know what’s what. Keep the order logical and don’t forget the paintbrush for snazzy colors. Here’s a data analysis presentation example on writers’ productivity using stacked bar charts:

7. Area chart

Similar to line charts but with the area below the lines filled, making them suitable for showing cumulative data.

Area charts are close cousins of line charts but come with a twist. 

Imagine plotting the sales of a product over several months. In an area chart, the space between the line and the x-axis is filled, providing a visual representation of the cumulative total. 

This makes it easy to see how values stack up over time, making area charts a valuable tool for tracking trends in data.

For area charts, use them to visualize cumulative data and trends, but avoid overcrowding the chart. Add labels, especially at significant points and make sure the area under the lines is filled with a visually appealing color gradient.

8. Tabular presentation

Presenting data in rows and columns, often used for precise data values and comparisons.

Tabular data presentation is all about clarity and precision. Think of it as presenting numerical data in a structured grid, with rows and columns clearly displaying individual data points. 

A table is invaluable for showcasing detailed data, facilitating comparisons and presenting numerical information that needs to be exact. They’re commonly used in reports, spreadsheets and academic papers.

When presenting tabular data, organize it neatly with clear headers and appropriate column widths. Highlight important data points or patterns using shading or font formatting for better readability.

9. Textual data

Utilizing written or descriptive content to explain or complement data, such as annotations or explanatory text.

Textual data presentation may not involve charts or graphs, but it’s one of the most used qualitative data presentation examples. 

It involves using written content to provide context, explanations or annotations alongside data visuals. Think of it as the narrative that guides your audience through the data. 

Well-crafted textual data can make complex information more accessible and help your audience understand the significance of the numbers and visuals.

Textual data is your chance to tell a story. Break down complex information into bullet points or short paragraphs and use headings to guide the reader’s attention.

10. Pictogram

Using simple icons or images to represent data is especially useful for conveying information in a visually intuitive manner.

Pictograms are all about harnessing the power of images to convey data in an easy-to-understand way. 

Instead of using numbers or complex graphs, you use simple icons or images to represent data points. 

For instance, you could use a thumbs up emoji to illustrate customer satisfaction levels, where each face represents a different level of satisfaction. 

Pictograms are great for conveying data visually, so choose symbols that are easy to interpret and relevant to the data. Use consistent scaling and a legend to explain the symbols’ meanings, ensuring clarity in your presentation.

Looking for more data presentation ideas? Use the Venngage graph maker or browse through our gallery of chart templates to pick a template and get started! 

A comprehensive data presentation should include several key elements to effectively convey information and insights to your audience. Here’s a list of what should be included in a data presentation:

1. Title and objective

• Begin with a clear and informative title that sets the context for your presentation.
• State the primary objective or purpose of the presentation to provide a clear focus.

2. Key data points

• Present the most essential data points or findings that align with your objective.
• Use charts, graphical presentations or visuals to illustrate these key points for better comprehension.

3. Context and significance

• Provide a brief overview of the context in which the data was collected and why it’s significant.
• Explain how the data relates to the larger picture or the problem you’re addressing.

4. Key takeaways

• Summarize the main insights or conclusions that can be drawn from the data.
• Highlight the key takeaways that the audience should remember.

5. Visuals and charts

• Use clear and appropriate visual aids to complement the data.
• Ensure that visuals are easy to understand and support your narrative.

6. Implications or actions

• Discuss the practical implications of the data or any recommended actions.
• If applicable, outline next steps or decisions that should be taken based on the data.

7. Q&A and discussion

• Allocate time for questions and open discussion to engage the audience.
• Address queries and provide additional insights or context as needed.

Presenting data is a crucial skill in various professional fields, from business to academia and beyond. To ensure your data presentations hit the mark, here are some common mistakes that you should steer clear of:

Overloading with data

Presenting too much data at once can overwhelm your audience. Focus on the key points and relevant information to keep the presentation concise and focused. Here are some free data visualization tools you can use to convey data in an engaging and impactful way. 

Assuming everyone’s on the same page

It’s easy to assume that your audience understands as much about the topic as you do. But this can lead to either dumbing things down too much or diving into a bunch of jargon that leaves folks scratching their heads. Take a beat to figure out where your audience is coming from and tailor your presentation accordingly.

Misleading visuals

Using misleading visuals, such as distorted scales or inappropriate chart types can distort the data’s meaning. Pick the right data infographics and understandable charts to ensure that your visual representations accurately reflect the data.

Not providing context

Data without context is like a puzzle piece with no picture on it. Without proper context, data may be meaningless or misinterpreted. Explain the background, methodology and significance of the data.

Not citing sources properly

Neglecting to cite sources and provide citations for your data can erode its credibility. Always attribute data to its source and utilize reliable sources for your presentation.

Not telling a story

Avoid simply presenting numbers. If your presentation lacks a clear, engaging story that takes your audience on a journey from the beginning (setting the scene) through the middle (data analysis) to the end (the big insights and recommendations), you’re likely to lose their interest.

Infographics are great for storytelling because they mix cool visuals with short and sweet text to explain complicated stuff in a fun and easy way. Create one with Venngage’s free infographic maker to create a memorable story that your audience will remember.

Ignoring data quality

Presenting data without first checking its quality and accuracy can lead to misinformation. Validate and clean your data before presenting it.

Simplify your visuals

Fancy charts might look cool, but if they confuse people, what’s the point? Go for the simplest visual that gets your message across. Having a dilemma between presenting data with infographics v.s data design? This article on the difference between data design and infographics might help you out. 

Missing the emotional connection

Data isn’t just about numbers; it’s about people and real-life situations. Don’t forget to sprinkle in some human touch, whether it’s through relatable stories, examples or showing how the data impacts real lives.

Skipping the actionable insights

At the end of the day, your audience wants to know what they should do with all the data. If you don’t wrap up with clear, actionable insights or recommendations, you’re leaving them hanging. Always finish up with practical takeaways and the next steps.

Can you provide some data presentation examples for business reports?

Business reports often benefit from data presentation through bar charts showing sales trends over time, pie charts displaying market share,or tables presenting financial performance metrics like revenue and profit margins.

What are some creative data presentation examples for academic presentations?

Creative data presentation ideas for academic presentations include using statistical infographics to illustrate research findings and statistical data, incorporating storytelling techniques to engage the audience or utilizing heat maps to visualize data patterns.

What are the key considerations when choosing the right data presentation format?

When choosing a chart format , consider factors like data complexity, audience expertise and the message you want to convey. Options include charts (e.g., bar, line, pie), tables, heat maps, data visualization infographics and interactive dashboards.

Knowing the type of data visualization that best serves your data is just half the battle. Here are some best practices for data visualization to make sure that the final output is optimized. 

How can I choose the right data presentation method for my data?

To select the right data presentation method, start by defining your presentation’s purpose and audience. Then, match your data type (e.g., quantitative, qualitative) with suitable visualization techniques (e.g., histograms, word clouds) and choose an appropriate presentation format (e.g., slide deck, report, live demo).

For more presentation ideas , check out this guide on how to make a good presentation or use a presentation software to simplify the process.  

How can I make my data presentations more engaging and informative?

To enhance data presentations, use compelling narratives, relatable examples and fun data infographics that simplify complex data. Encourage audience interaction, offer actionable insights and incorporate storytelling elements to engage and inform effectively.

The opening of your presentation holds immense power in setting the stage for your audience. To design a presentation and convey your data in an engaging and informative, try out Venngage’s free presentation maker to pick the right presentation design for your audience and topic. 

What is the difference between data visualization and data presentation?

Data presentation typically involves conveying data reports and insights to an audience, often using visuals like charts and graphs. Data visualization , on the other hand, focuses on creating those visual representations of data to facilitate understanding and analysis. 

Now that you’ve learned a thing or two about how to use these methods of data presentation to tell a compelling data story , it’s time to take these strategies and make them your own. 

But here’s the deal: these aren’t just one-size-fits-all solutions. Remember that each example we’ve uncovered here is not a rigid template but a source of inspiration. It’s all about making your audience go, “Wow, I get it now!”

Think of your data presentations as your canvas – it’s where you paint your story, convey meaningful insights and make real change happen. 

So, go forth, present your data with confidence and purpose and watch as your strategic influence grows, one compelling presentation at a time.

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• Diagrammatic Presentation Of Data

Diagrammatic Presentation of Data

The diagrammatic presentation of data gives an immediate understanding of the real situation to be defined by the data in comparison to the tabular presentation of data or textual representations. It translates the highly complex ideas included in numbers into a more concrete and quickly understandable form pretty effectively. Diagrams may be less certain but are much more efficient than tables in displaying the data. There are many kinds of diagrams in general use. Amongst them the significant ones are the following:

(i) Geometric diagram

(ii) Frequency diagram

(iii) Arithmetic line graph

Also check: Meaning and Objective of Tabulation

Basics of Diagrammatic Presentation

Concept of Diagrammatic Presentation

• It is a technique of presenting numeric data through pictograms, cartograms, bar diagrams, and pie diagrams. It is the most attractive and appealing way to represent statistical data. Diagrams help in visual comparison and they have a bird’s eye view.
• Under pictograms, we use pictures to present data. For example, if we have to show the production of cars, we can draw cars. Suppose the production of cars is 40,000, we can show it by a picture having four cars, where 1 car represents 10,000 units.
• Under cartograms, we make use of maps to show the geographical allocation of certain things.
• Bar diagrams are rectangular and placed on the same base. Their heights represent the magnitude/value of the variable. The width of all the bars and the gaps between the two bars are kept the same.
• Pie diagram is a circle that is subdivided or partitioned to show the proportion of various components of the data.
• Out of the given diagrams, only one-dimensional bar diagrams and pie diagrams are there in our scope.

General Guidelines

Title: Every diagram must be given a suitable title which should be small and self-explanatory.

Size: The size of the diagram should be appropriate, i.e., neither too small nor too big.

Paper used: Diagrams are generally prepared on blank paper.

Scale: Under one-dimensional diagrams, especially bar diagrams, the y-axis is more important from the point of view of the decision of scale because we represent magnitude along this axis.

Index: When two or more variables are presented and different types of line/shading patterns are used to distinguish, an index must be given to show their details.

Selection of proper type of diagram: It is very important to select the correct type of diagram to represent data effectively.

Advantages of Diagrammatic Presentation

(1) Diagrams are attractive and impressive:   The data presented in the form of diagrams can attract the attention of even a common man.

(2) Easy to remember:    (a)  Diagrams have a great memorising effect. (b)  The picture created in mind by the diagrams last much longer than those created by figures presented through the tabular forms.

(3) Diagrams save time : (a)  They present complex mass data in a simplified manner. (b)  The data presented in the form of diagrams can be understood by the user very quickly.

(4) Diagrams simplify data:   Diagrams are used to represent a huge mass of complex data in a simplified and intelligible form which is easy to understand.

(5) Diagrams are useful in making comparison:   It becomes easier to compare two sets of data visually by presenting them through diagrams.

(6) More informative :   Diagrams not only depict the characteristics of data but also bring out other hidden facts and relations which are not possible from the classified and tabulated data.

Types of One-Dimensional Diagram

One-dimensional diagram is a diagram in which only the length of the diagram is considered. It can be drawn in the form of a line or various types of bars.

The following are the types of one-dimensional diagram.

(1) Simple bar diagram

Simple bar diagram consists of a group of rectangular bars of equal width for each class or category of data.

(2) Multiple bar diagram

This diagram is used when we have to make a comparison between two or more variables like income and expenditure, import and export for different years, marks obtained in different subjects in different classes, etc.

(3) Subdivided bar diagram

This diagram is constructed by subdividing the bars in the ratio of various components.

(4) Percentage bar diagram

The subdivided bar diagram presented on a percentage basis is known as the percentage bar diagram.

(5) Broken-scale bar diagram

This diagram is used when the value of one observation is very high as compared to the other.

To gain space for the smaller bars of the series, the larger bars may be broken.

The value of each bar is written at the top of the bar.

(6) Deviation bar diagram

Deviation bars are used to represent net changes in the data like net profit, net loss, net exports, net imports, etc.

Meaning of Pie Diagram

A pie diagram is a circle that is divided into sections. The size of each section indicates the magnitude of each component as a part of the whole.

Steps involved in constructing pie diagram

• Convert the given values into percentage form and multiply it with 3.6’ to get the amount of angle for each item.
• Draw a circle and start the diagram at the 12 O‘clock position.
• Take the highest angle first with the protector (D) and mark the lower angles successively.
• Shade different angles differently to show distinction in each item.

Solved Questions

Q.1. Why is a diagrammatic presentation better than tabulation of data?

It makes the data more attractive as compared to tabulation and helps in visual comparison.

Q.2. Why do media persons prefer diagrammatic presentation of data?

Because it has an eye-catching effect and a long-lasting impact upon its readers/viewers.

Q.3. What will be the degree of an angle in the pie diagram if a family spends 50% of its income in food?

(50 ÷ 100) X 360 (Or) 50 x 3.6 = 180’

Q.4. Which bar diagram is used to show two or more characteristics of the data?

Multiple bar diagram

Q.5. Mention the sum of all the angles formed at the centre of a circle.

Q.6. Name a bar diagram where the height of all the bars is the same.

Percentage bar diagram

Q.7. Which diagram can be used to depict various components of a variable?

Subdivided bar diagram

Q.8. What is a multiple bar diagram?

A multiple bar diagram is one that shows more than one characteristic of data.

Q.9. Which bar diagram is used to represent the net changes in data?

Deviation bar diagram

Q.10. What is the other name of the subdivided bar Diagram?

Component bar diagram

The above-mentioned concept is for CBSE Class 11 Statistics for Economics – Diagrammatic Presentation of Data. For solutions and study materials, visit our website or download the app for more information and the best learning experience.

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Reference Examples

More than 100 reference examples and their corresponding in-text citations are presented in the seventh edition Publication Manual . Examples of the most common works that writers cite are provided on this page; additional examples are available in the Publication Manual .

To find the reference example you need, first select a category (e.g., periodicals) and then choose the appropriate type of work (e.g., journal article ) and follow the relevant example.

When selecting a category, use the webpages and websites category only when a work does not fit better within another category. For example, a report from a government website would use the reports category, whereas a page on a government website that is not a report or other work would use the webpages and websites category.

Also note that print and electronic references are largely the same. For example, to cite both print books and ebooks, use the books and reference works category and then choose the appropriate type of work (i.e., book ) and follow the relevant example (e.g., whole authored book ).

Examples on these pages illustrate the details of reference formats. We make every attempt to show examples that are in keeping with APA Style’s guiding principles of inclusivity and bias-free language. These examples are presented out of context only to demonstrate formatting issues (e.g., which elements to italicize, where punctuation is needed, placement of parentheses). References, including these examples, are not inherently endorsements for the ideas or content of the works themselves. An author may cite a work to support a statement or an idea, to critique that work, or for many other reasons. For more examples, see our sample papers .

Reference examples are covered in the seventh edition APA Style manuals in the Publication Manual Chapter 10 and the Concise Guide Chapter 10

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Data sets are covered in Section 10.9 of the Publication Manual . For the software and tests categories, see Sections 10.10 and 10.11.

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Audiovisual media are covered in Sections 10.12–10.14 of the Publication Manual . The most common examples are presented together here. In the manual, these examples and more are separated into categories for audiovisual, audio, and visual media.

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Online media are covered in Sections 10.15 and 10.16 of the Publication Manual . Please note that blog posts are part of the periodicals category.

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Introducing Apple Intelligence, the personal intelligence system that puts powerful generative models at the core of iPhone, iPad, and Mac

New Capabilities for Understanding and Creating Language

Image Playground Makes Communication and Self‑Expression Even More Fun

Genmoji Creation to Fit Any Moment

New Features in Photos Give Users More Control

Siri Enters a New Era

A New Standard for Privacy in AI

ChatGPT Gets Integrated Across Apple Platforms

Text of this article

June 10, 2024

PRESS RELEASE

Setting a new standard for privacy in AI, Apple Intelligence understands personal context to deliver intelligence that is helpful and relevant

CUPERTINO, CALIFORNIA Apple today introduced Apple Intelligence , the personal intelligence system for iPhone, iPad, and Mac that combines the power of generative models with personal context to deliver intelligence that’s incredibly useful and relevant. Apple Intelligence is deeply integrated into iOS 18, iPadOS 18, and macOS Sequoia. It harnesses the power of Apple silicon to understand and create language and images, take action across apps, and draw from personal context to simplify and accelerate everyday tasks. With Private Cloud Compute, Apple sets a new standard for privacy in AI, with the ability to flex and scale computational capacity between on-device processing and larger, server-based models that run on dedicated Apple silicon servers.

“We’re thrilled to introduce a new chapter in Apple innovation. Apple Intelligence will transform what users can do with our products — and what our products can do for our users,” said Tim Cook, Apple’s CEO. “Our unique approach combines generative AI with a user’s personal context to deliver truly helpful intelligence. And it can access that information in a completely private and secure way to help users do the things that matter most to them. This is AI as only Apple can deliver it, and we can’t wait for users to experience what it can do.”

Apple Intelligence unlocks new ways for users to enhance their writing and communicate more effectively. With brand-new systemwide Writing Tools built into iOS 18, iPadOS 18, and macOS Sequoia, users can rewrite, proofread, and summarize text nearly everywhere they write, including Mail, Notes, Pages, and third-party apps.

Whether tidying up class notes, ensuring a blog post reads just right, or making sure an email is perfectly crafted, Writing Tools help users feel more confident in their writing. With Rewrite, Apple Intelligence allows users to choose from different versions of what they have written, adjusting the tone to suit the audience and task at hand. From finessing a cover letter, to adding humor and creativity to a party invitation, Rewrite helps deliver the right words to meet the occasion. Proofread checks grammar, word choice, and sentence structure while also suggesting edits — along with explanations of the edits — that users can review or quickly accept. With Summarize, users can select text and have it recapped in the form of a digestible paragraph, bulleted key points, a table, or a list.

In Mail, staying on top of emails has never been easier. With Priority Messages, a new section at the top of the inbox shows the most urgent emails, like a same-day dinner invitation or boarding pass. Across a user’s inbox, instead of previewing the first few lines of each email, they can see summaries without needing to open a message. For long threads, users can view pertinent details with just a tap. Smart Reply provides suggestions for a quick response, and will identify questions in an email to ensure everything is answered.

Deep understanding of language also extends to Notifications. Priority Notifications appear at the top of the stack to surface what’s most important, and summaries help users scan long or stacked notifications to show key details right on the Lock Screen, such as when a group chat is particularly active. And to help users stay present in what they’re doing, Reduce Interruptions is a new Focus that surfaces only the notifications that might need immediate attention, like a text about an early pickup from daycare.

In the Notes and Phone apps, users can now record, transcribe, and summarize audio. When a recording is initiated while on a call, participants are automatically notified, and once the call ends, Apple Intelligence generates a summary to help recall key points.

Apple Intelligence powers exciting image creation capabilities to help users communicate and express themselves in new ways. With Image Playground, users can create fun images in seconds, choosing from three styles: Animation, Illustration, or Sketch. Image Playground is easy to use and built right into apps including Messages. It’s also available in a dedicated app, perfect for experimenting with different concepts and styles. All images are created on device, giving users the freedom to experiment with as many images as they want.

With Image Playground, users can choose from a range of concepts from categories like themes, costumes, accessories, and places; type a description to define an image; choose someone from their personal photo library to include in their image; and pick their favorite style.

With the Image Playground experience in Messages, users can quickly create fun images for their friends, and even see personalized suggested concepts related to their conversations. For example, if a user is messaging a group about going hiking, they’ll see suggested concepts related to their friends, their destination, and their activity, making image creation even faster and more relevant.

In Notes, users can access Image Playground through the new Image Wand in the Apple Pencil tool palette, making notes more visually engaging. Rough sketches can be turned into delightful images, and users can even select empty space to create an image using context from the surrounding area. Image Playground is also available in apps like Keynote, Freeform, and Pages, as well as in third-party apps that adopt the new Image Playground API.

Taking emoji to an entirely new level, users can create an original Genmoji to express themselves. By simply typing a description, their Genmoji appears, along with additional options. Users can even create Genmoji of friends and family based on their photos. Just like emoji, Genmoji can be added inline to messages, or shared as a sticker or reaction in a Tapback.

Searching for photos and videos becomes even more convenient with Apple Intelligence. Natural language can be used to search for specific photos, such as “Maya skateboarding in a tie-dye shirt,” or “Katie with stickers on her face.” Search in videos also becomes more powerful with the ability to find specific moments in clips so users can go right to the relevant segment. Additionally, the new Clean Up tool can identify and remove distracting objects in the background of a photo — without accidentally altering the subject.

With Memories, users can create the story they want to see by simply typing a description. Using language and image understanding, Apple Intelligence will pick out the best photos and videos based on the description, craft a storyline with chapters based on themes identified from the photos, and arrange them into a movie with its own narrative arc. Users will even get song suggestions to match their memory from Apple Music. As with all Apple Intelligence features, user photos and videos are kept private on device and are not shared with Apple or anyone else.

Powered by Apple Intelligence, Siri becomes more deeply integrated into the system experience. With richer language-understanding capabilities, Siri is more natural, more contextually relevant, and more personal, with the ability to simplify and accelerate everyday tasks. It can follow along if users stumble over words and maintain context from one request to the next. Additionally, users can type to Siri, and switch between text and voice to communicate with Siri in whatever way feels right for the moment. Siri also has a brand-new design with an elegant glowing light that wraps around the edge of the screen when Siri is active.

Siri can now give users device support everywhere they go, and answer thousands of questions about how to do something on iPhone, iPad, and Mac. Users can learn everything from how to schedule an email in the Mail app, to how to switch from Light to Dark Mode.

With onscreen awareness, Siri will be able to understand and take action with users’ content in more apps over time. For example, if a friend texts a user their new address in Messages, the receiver can say, “Add this address to his contact card.”

With Apple Intelligence, Siri will be able to take hundreds of new actions in and across Apple and third-party apps. For example, a user could say, “Bring up that article about cicadas from my Reading List,” or “Send the photos from the barbecue on Saturday to Malia,” and Siri will take care of it.

Siri will be able to deliver intelligence that’s tailored to the user and their on-device information. For example, a user can say, “Play that podcast that Jamie recommended,” and Siri will locate and play the episode, without the user having to remember whether it was mentioned in a text or an email. Or they could ask, “When is Mom’s flight landing?” and Siri will find the flight details and cross-reference them with real-time flight tracking to give an arrival time.

To be truly helpful, Apple Intelligence relies on understanding deep personal context while also protecting user privacy. A cornerstone of Apple Intelligence is on-device processing, and many of the models that power it run entirely on device. To run more complex requests that require more processing power, Private Cloud Compute extends the privacy and security of Apple devices into the cloud to unlock even more intelligence.

With Private Cloud Compute, Apple Intelligence can flex and scale its computational capacity and draw on larger, server-based models for more complex requests. These models run on servers powered by Apple silicon, providing a foundation that allows Apple to ensure that data is never retained or exposed.

Independent experts can inspect the code that runs on Apple silicon servers to verify privacy, and Private Cloud Compute cryptographically ensures that iPhone, iPad, and Mac do not talk to a server unless its software has been publicly logged for inspection. Apple Intelligence with Private Cloud Compute sets a new standard for privacy in AI, unlocking intelligence users can trust.

Apple is integrating ChatGPT access into experiences within iOS 18, iPadOS 18, and macOS Sequoia, allowing users to access its expertise — as well as its image- and document-understanding capabilities — without needing to jump between tools.

Siri can tap into ChatGPT’s expertise when helpful. Users are asked before any questions are sent to ChatGPT, along with any documents or photos, and Siri then presents the answer directly.

Additionally, ChatGPT will be available in Apple’s systemwide Writing Tools, which help users generate content for anything they are writing about. With Compose, users can also access ChatGPT image tools to generate images in a wide variety of styles to complement what they are writing.

Privacy protections are built in for users who access ChatGPT — their IP addresses are obscured, and OpenAI won’t store requests. ChatGPT’s data-use policies apply for users who choose to connect their account.

ChatGPT will come to iOS 18, iPadOS 18, and macOS Sequoia later this year, powered by GPT-4o. Users can access it for free without creating an account, and ChatGPT subscribers can connect their accounts and access paid features right from these experiences.

Availability

Apple Intelligence is free for users, and will be available in beta as part of iOS 18 , iPadOS 18 , and macOS Sequoia  this fall in U.S. English. Some features, software platforms, and additional languages will come over the course of the next year. Apple Intelligence will be available on iPhone 15 Pro, iPhone 15 Pro Max, and iPad and Mac with M1 and later, with Siri and device language set to U.S. English. For more information, visit apple.com/apple-intelligence .

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