Presentation of Data Class 11 Notes

Q: Q10 Draw the angles for a pie diagram from: rent ₹12,000, food ₹18,000, savings ₹6,000, other ₹24,000.

The angles are 72°, 108°, 36° and 144°. Given: total = 12,000 + 18,000 + 6,000 + 24,000 = 60,000. Formula: angle = value ÷ total × 360°. Steps: rent 12/60 × 360 = 72°; food 18/60 × 360 = 108°; savings 6/60 × 360 = 36°; other 24/60 × 360 = 144°. Final answer: 72°, 108°, 36°, 144°; the sum is 360°.

Key takeaways

Use text for a few figures, tables to compare many and diagrams for quick impact.
A table needs a title, captions, stubs, body, unit and source.
Pie angle = per cent × 3.6°.
A histogram has touching bars; use frequency density when class widths differ.
The less-than and more-than ogives intersect at the median.

This is Chapter 4 of the Statistics for Economics chapter list for Class 11 Economics. It builds on the tables of Chapter 3.

4.1Textual Presentation

Textual presentation conveys data in sentences within a paragraph. It suits a few figures and keeps the numbers in context, such as a sentence noting that a school has 480 students of whom 55 per cent are girls. It becomes confusing when many figures must be compared, where tables and charts work better.

A line such as “Of 30 students surveyed, 20 study for 8 hours or more a week and 10 for less” gives the key finding quickly. Its weakness is that the reader must pick out and compare the numbers unaided. Use text for a few figures and for interpretation, and move larger sets into tables.

When text is enough

Text works well for a few figures and for stating a conclusion. A sentence such as “Of 30 students surveyed, 20 study eight hours or more a week” is clearer than a table of two numbers. Text is also needed to explain what a table or chart shows, to give the unit and period, and to say what the reader should notice.

Long paragraphs with many numbers are hard to follow, because the reader has to compare them mentally. Once there are more than four or five figures, move them into a table and keep the text for interpretation.

4.2Tabular Presentation

Tabulation arranges data in rows and columns so figures can be compared and read quickly. A good table has a number and title, column captions, row stubs, a body of figures, the unit of measurement and the source. Tables may classify data by quality, quantity, time or place.

Parts of a table

Parts of a statistical table
Part	What it holds
Table number	Identifies the table for reference
Title	Says what, where and when, briefly
Captions	Column headings
Stubs	Row headings
Body	The figures themselves
Unit of measurement	For example ₹ crore, per cent, tonnes
Source note and footnote	Where the data came from; any exceptions

Tables by type of classification

A qualitative table classes data by an attribute such as sex; a quantitative table by a measured value such as marks; a temporal table by time; a spatial table by place. The frequency table in Chapter 3 is a quantitative table.

Table 4.1: Sources of income in a village, per cent (illustrative)
Source	Share of income (%)
Farming	45
Wage work	25
Business	18
Other	12
Total	100

Source: illustrative figures created for this page.

Designing a clear table

A clear table puts the items to be compared next to each other and arranges rows in a meaningful order, such as by size or by time. Units are placed in the title or column heading, and totals are included when they help. Lines and shading should be light, so that the figures stand out. Numbers are aligned, and the same number of decimals is used for similar values.

A footnote explains special cases, such as provisional figures. A source note allows readers to trace the data. A table that is cluttered, or that lacks a title, unit or source, cannot be used with confidence.

A method for reading a table

Start with the title, the unit and the source, so that you know what is measured and who reports it. Read the headings of rows and columns, then look at the largest and smallest values and at totals. Compare rows or columns by percentage rather than by raw numbers when the totals differ. Finally, state in one sentence what the table shows.

This habit helps in examinations as well as in real life, because many mistakes come from reading a figure without checking its unit or period.

4.3Diagrammatic Presentation

Diagrams turn numbers into pictures that are quick to grasp and remember. Common diagrams are the simple, multiple and component bar diagram and the pie diagram. Bars compare sizes, while a pie diagram shows how a total is divided, with each slice's angle equal to its percentage multiplied by 3.6 degrees.

Bar diagrams

Types of bar diagram
Type	Shows	Use
Simple	One value per bar	Compare one variable across categories
Multiple	Bars side by side	Compare two or more variables, such as boys and girls
Component (stacked)	Each bar divided into parts	Show both total and its composition

Bars should have equal width, a common baseline starting at zero, and clear labels; a truncated baseline exaggerates differences.

Pie diagram

A pie diagram divides a circle in proportion to the shares. Since a full circle is 360°, angle = (value ÷ total) × 360°, or per cent × 3.6°.

Figure 4.1: Pie diagramShares of village income (illustrative). The four angles add to 360°.

Good and misleading charts

A good chart has a title, labelled axes with units, a zero baseline for bars, and a clear choice of colours or patterns. It shows only as much as the reader can take in. A misleading chart may cut the vertical axis so that small differences look large, use three-dimensional effects that distort areas, or squeeze or stretch the scale of one axis.

Always check the axis values before drawing conclusions from a chart, and when drawing one, choose the type that matches the message: bars to compare, pies for shares of a whole, lines for changes over time.

4.4Graphs: Histogram, Polygon, Ogive and Time Series

A histogram shows a frequency distribution as touching bars whose areas are proportional to frequencies. A frequency polygon joins the mid-points of the bar tops. An ogive plots cumulative frequency and, when drawn both ways, cuts at the median. A time series graph plots values against time.

Histogram and frequency polygon

For a continuous variable the bars touch, because the classes have no gaps. If class widths are unequal, plot frequency density (frequency ÷ class width) so area stays proportional to frequency. A frequency polygon joins the class marks, closed at both ends on the axis. The tallest bar of a histogram points to the mode.

Figure 4.2: Histogram with frequency polygonWeekly study hours of 30 students: heights 1, 9, 11, 8 and 1. The polygon runs from 0 to 20 through the class marks 2, 6, 10, 14 and 18.

Ogives

An ogive plots cumulative frequency against class limits. The less-than ogive uses upper limits and rises; the more-than ogive uses lower limits and falls. The two cross at the median. Reading across from half the total gives the median directly.

Figure 4.3: Less-than ogiveCumulative frequency 1, 10, 21, 29 and 30 at upper limits 4, 8, 12, 16 and 20. Half of 30 is 15, which reads across to a median of about 9.82 hours.

Time series graph

A time series graph (arithmetic line graph) plots a variable such as monthly rainfall against time and joins the points. It shows trends, seasonal swings and sudden breaks at a glance.

Choosing between a histogram and a polygon

A histogram shows the shape of a single distribution clearly because each bar represents a class. A frequency polygon, made by joining the mid-points of the bars, is better for comparing two or more distributions on the same axes, since lines can overlap without hiding one another. A frequency curve is a smooth version that suggests the underlying shape.

Whichever is used, the classes must be continuous, with no gaps, and the horizontal axis must show the class limits or boundaries. For open-ended classes a polygon cannot be closed, so the data need a sensible assumption first.

Reading values from an ogive

An ogive allows quick answers to questions that would otherwise need calculation. To find how many students study fewer than 10 hours, read upwards from 10 on the horizontal axis to the curve and then across to the vertical axis. To find the median, start at half the total frequency on the vertical axis and read across and down. The quartiles are found in the same way from one-quarter and three-quarters of the total.

Readings from a graph are approximate, and the formula gives a more exact value, but the graph shows the pattern at a glance and helps check the calculation.

Worked Examples

Example 1: Angles of a pie diagram

Given: Sources of village income: farming 45%, wage work 25%, business 18%, other 12%.
Formula: Angle = per cent × 3.6°
Steps: 45 × 3.6 = 162°; 25 × 3.6 = 90°; 18 × 3.6 = 64.8°; 12 × 3.6 = 43.2°. Check: 162 + 90 + 64.8 + 43.2 = 360.
Answer: The angles are 162°, 90°, 64.8° and 43.2°.

Example 2: Frequency density for unequal classes

Given: Class 0–10: 20 workers; 10–30: 60 workers; 30–40: 30 workers. Standard width = 10.
Formula: Adjusted frequency = frequency ÷ class width × standard width
Steps: 0–10: 20 ÷ 10 × 10 = 20. 10–30: 60 ÷ 20 × 10 = 30. 30–40: 30 ÷ 10 × 10 = 30.
Answer: Plot heights 20, 30 and 30; the 10–30 class would otherwise look twice as tall as it is.

Example 3: Median from an ogive

Given: Cumulative frequencies 1, 10, 21, 29 and 30 at upper limits 4, 8, 12, 16 and 20; N = 30.
Formula: Median = L + (N ÷ 2 − c.f.) ÷ f × h
Steps: N ÷ 2 = 15 lies in the class 8–12. L = 8, c.f. = 10, f = 11, h = 4. Median = 8 + (15 − 10) ÷ 11 × 4 = 8 + 1.82.
Answer: The median is about 9.82 hours, matching the ogive.

Common Mistakes

Starting a bar diagram's axis above zero. It makes small differences look large.
Leaving gaps between bars of a histogram for a continuous variable; the bars should touch.
Plotting raw frequency instead of frequency density when class widths are unequal.
Forgetting the unit, title or source on a table or chart.

10 Important Questions for Class 11 Board and School Examinations

Questions are written in original words. Marks are shown beside each question.

Q1The angle for a 20 per cent slice of a pie diagram is (a) 20° (b) 36° (c) 72° (d) 90° 1 mark · MCQ

The correct option is (c) 72°, since 20 × 3.6 = 72.

Q2The two ogives (less-than and more-than) intersect at the (a) mean (b) mode (c) median (d) range 1 mark · MCQ

The correct option is (c) the median.

Q3Assertion (A): Bars of a histogram touch each other. Reason (R): Histograms are drawn for continuous classes with no gaps. Which is correct? 1 mark · Assertion-reason

Both A and R are true, and R explains A.

Q4What are the parts of a statistical table? Name any five. 3 marks

A statistical table has a number, title, captions, stubs, body, unit and source.

Title: says what, where and when, briefly.
Captions are column headings and stubs are row headings.
Body: the figures themselves.
Unit of measurement and source note, so readers can verify the figures.

Footnotes explain exceptions.

These parts make a table self-explanatory. A good table also arranges rows and columns so that comparisons are easy, and may include totals.

Q5Distinguish between a histogram and a bar diagram. 3 marks

A histogram shows a continuous frequency distribution with touching bars, while a bar diagram compares separate categories with gaps between bars.

In a histogram the area of each bar represents frequency, so the width of the class matters, and unequal classes need frequency density. In a bar diagram only the height matters and all bars have equal width. A histogram suits grouped numerical data such as marks, whereas a bar diagram suits items such as the output of different crops.

Q6Explain how a pie diagram is constructed. Show the angles for shares of 50, 30 and 20 per cent. 4 marks

A pie diagram divides a circle of 360 degrees in proportion to the shares of the parts.

Find each share as a percentage of the total.
Angle = per cent × 3.6°, or value ÷ total × 360°.
For shares of 50, 30 and 20 per cent the angles are 180°, 108° and 72°, which add to 360°.
Draw the slices in order and label each with its share.

A pie diagram suits data with only a few parts, since many thin slices are hard to read.

Q7How are a frequency polygon and an ogive drawn? 4 marks

A frequency polygon joins the class marks plotted against frequencies, while an ogive joins cumulative frequencies plotted against class limits.

Polygon: plot the mid-point of each class with its frequency, join the points with straight lines and close the figure at both ends on the axis.
Less-than ogive: plot upper limits against cumulative frequency; it rises from left to right.
More-than ogive: plot lower limits against reverse cumulative frequency; it falls.
The two ogives cross at the median.

Reading across from half the total on the ogive gives the median directly.

Q8Compare textual, tabular and diagrammatic presentation of data. 6 marks

Text suits a few figures, tables suit comparing many, and diagrams suit quick visual understanding.

Textual: easy to write and keeps figures in context, but numbers are hard to compare.
Tabular: precise and compact, but needs study to read.
Diagrammatic: attractive and quick to grasp, and good for comparison and trends, but less exact.
Choose the method according to the audience and purpose.

Often a table and a chart are used together, with a few sentences of text pointing out the main finding.

The choice also depends on how much precision the reader needs. For an examination answer, a short sentence on the main finding followed by a table or diagram is often the clearest. Diagrams should have a title, labelled axes with units, and a source, just as tables do. Misleading scales or crowded charts defeat the purpose of presenting data.

Q9Explain the three types of bar diagram with a situation where each is useful. 6 marks

Simple, multiple and component bar diagrams serve different comparisons.

Simple bar diagram: one value per bar, such as the output of five crops.
Multiple bar diagram: bars side by side, such as boys and girls enrolled in each year.
Component bar diagram: each bar split into parts, such as total household spending divided into food, housing and other items.
All need a baseline at zero, bars of equal width and clear labels.

A truncated axis exaggerates differences and should be avoided.

A simple bar diagram suits comparing a single variable, a multiple bar diagram for comparing two or three variables over time or between groups, and a component bar diagram when the total and its parts both matter. Component bars may also be drawn in per cent form, so that bars of different totals can be compared on the same scale.

Q10Draw the angles for a pie diagram from: rent ₹12,000, food ₹18,000, savings ₹6,000, other ₹24,000. 4 marks · Numerical

The angles are 72°, 108°, 36° and 144°.

Given: total = 12,000 + 18,000 + 6,000 + 24,000 = 60,000.

Formula: angle = value ÷ total × 360°.

Steps: rent 12/60 × 360 = 72°; food 18/60 × 360 = 108°; savings 6/60 × 360 = 36°; other 24/60 × 360 = 144°.

Final answer: 72°, 108°, 36°, 144°; the sum is 360°.

10 Points for State PSC and UPSC Aspirants

The Lorenz curve is a cumulative graph of income shares, drawn like an ogive and used to read inequality.Why it matters: a graphical link with Chapter 3 and with the Gini coefficient.Source: NCERT; standard economics textbooks
The Economic Survey presents most macro indicators as tables and time series graphs.Why it matters: reading such presentations is expected in mains answers.Source: Economic Survey
Official tables carry a title, unit and source note, and often use footnotes to flag provisional or revised numbers.Why it matters: check provisional versus revised estimates before quoting.Source: MoSPI
A time series of GDP at constant prices shows growth trends better than one at current prices.Why it matters: choosing the right series matters in analysis.Source: MoSPI; Economic Survey
Pie diagrams are common for the composition of GDP by sector or of the Union Budget by receipts and expenditure.Why it matters: the Budget “Rupee Comes From / Goes To” chart is a pie-type diagram.Source: Union Budget documents
The Union Budget publishes the “Rupee Comes From / Goes To” diagrams in its At a Glance document.Why it matters: an official example of component presentation.Source: indiabudget.gov.in
A truncated axis is a known way of making small changes look large; examiners expect you to recognise it.Why it matters: a classic point in critique-of-data questions.Source: NCERT
Open data portals publish datasets as downloadable tables for user-built charts.Why it matters: supports evidence-based answers.Source: NITI Aayog; data.gov.in
A histogram of household expenditure shows how many households fall in each spending class.Why it matters: a graphical use of NSS data.Source: MoSPI
Frequency density must be used when class widths differ, otherwise areas mislead.Why it matters: a common numerical trap.Source: NCERT

These are revision notes, not official predictions of exam content.

Quick Revision

Text, tables and diagrams are the three modes.
Table parts: title, captions, stubs, body, unit, source.
Bar: equal widths, zero baseline.
Pie angle = per cent × 3.6°.
Histogram bars touch; use frequency density for unequal widths.
Polygon joins class marks.
Ogives cross at the median.

Glossary:

Histogram Ogive Frequency distribution Pie diagram

Related chapters: Organisation of Data, the source of every frequency table drawn here; Measures of Central Tendency, which summarises the same data in one number.

Sources

NCERT textbooks: Statistics for Economics, Class 11, National Council of Educational Research and Training. Syllabus reference. Accessed 23 October 2026.
Ministry of Statistics and Programme Implementation (MoSPI), Government of India. Accessed 23 October 2026.
Union Budget, Ministry of Finance, Government of India. Accessed 23 October 2026.
NITI Aayog, Government of India. Accessed 23 October 2026.
Press Information Bureau, Government of India. Accessed 23 October 2026.

About this page

Drafted with AI assistance from the NCERT chapter structure, in original words. Content is checked and approved by Dr. Anamika Shrivastava, PhD Economics, before publication. Read how this site works or send a correction.

Syllabus year 2026-27 · Last updated 23 October 2026