NCERT Solutions for Class 11 Economics Chapter 4: Presentation of Data

These Class 11 Economics Chapter 4 solutions cover Presentation of Data from the NCERT textbook Statistics for Economics (2026–27 session). The chapter explains the three main forms of presenting statistical data — textual, tabular and diagrammatic — the parts of a good statistical table, and the various diagrams (bar diagrams, pie chart, histogram, frequency polygon, frequency curve, ogive and arithmetic line graph). Below you get every NCERT exercise question reproduced verbatim and solved step by step, with tables and diagrams described in words, plus key terms, formulas, extra practice, MCQs, Assertion–Reason and FAQs.

Class: 11 Subject: Economics Book: Statistics for Economics Chapter: 4 Chapter Name: Presentation of Data Session: 2026–27
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Class 11 Economics Chapter 4 – Overview

Chapter 4, Presentation of Data, deals with putting collected and organised data into a compact, readable form so that voluminous information can be understood quickly. There are three forms of presentation. In textual (descriptive) presentation, data are described within the running text — suitable only when the quantity of data is small. In tabular presentation, data are arranged systematically in rows and columns; classification may be qualitative, quantitative, temporal (by time) or spatial (by place), and a good table has eight parts — table number, title, captions, stubs, body, unit, source and note. In diagrammatic presentation, data are shown through diagrams that give the quickest understanding: geometric diagrams (simple, multiple and component bar diagrams, and pie diagram), frequency diagrams (histogram, frequency polygon, frequency curve and ogive) and the arithmetic line graph (time series graph). The chapter also shows how a histogram locates the mode and how the two ogives intersect at the median.

Key Concepts & Terms

Textual presentation: data described within the text; useful only when the quantity of data is not too large, since the whole text must be read for comprehension.

Tabular presentation: data arranged in rows (read horizontally) and columns (read vertically); its main advantage is that it organises data for further statistical treatment and decision-making.

Qualitative classification: data classified according to attributes such as sex, location, nationality or social status.

Quantitative classification: data classified on the basis of measurable characteristics such as age, height, income or production, using class limits.

Temporal classification: time (hours, days, months, years) is the classifying variable.

Spatial classification: classification is done on the basis of place — village, town, district, state or country.

Parts of a table: (i) table number, (ii) title, (iii) captions/column headings, (iv) stubs/row headings, (v) body of the table, (vi) unit of measurement, (vii) source and (viii) note.

Geometric diagrams: bar diagram and pie diagram. Bar diagrams are of three types — simple, multiple (compares two or more sets of data) and component (shows a bar divided into its parts).

Pie diagram: a circle whose area is proportionally divided among the components; each percentage is converted into an angle by multiplying by 3.6°.

Frequency diagrams: histogram, frequency polygon, frequency curve and ogive — used for grouped frequency distributions. A histogram is drawn only for continuous variables; its area is proportional to class frequency.

Ogive (cumulative frequency curve): two types — ‘less than’ (plotted against upper class limits, never decreasing) and ‘more than’ (plotted against lower class limits, never increasing); the two ogives intersect at the median.

Arithmetic line graph (time series graph): time is plotted on the X-axis and the value of the variable on the Y-axis; it helps in understanding the trend, periodicity, etc., in long-term data.

Important Formulas & Formats

Pie diagram — angle of a component: Angle = Percentage of the component × 3.6°  (since 360° ÷ 100 = 3.6° per 1%).

Percentage of a component: Percentage = (Value of component ÷ Total value) × 100.

Frequency density (for unequal class widths in a histogram): Frequency density = Class frequency ÷ Width of the class interval. Rectangle heights use frequency density so that areas remain proportional to frequencies.

Graphical results: Mode → located from a histogram (x-coordinate of the peak rectangle); Median → located at the intersection of the ‘less than’ and ‘more than’ ogives.

NCERT “Exercises” — Full Solutions

All questions below are reproduced verbatim from the NCERT textbook’s end-of-chapter Exercises. Answers are original; diagrams are described in words from the given data.

Answer the following questions, 1 to 10, choosing the correct answer.

1. Bar diagram is a (i) one-dimensional diagram (ii) two-dimensional diagram (iii) diagram with no dimension (iv) none of the above

ANSWER (i) one-dimensional diagram. In a bar diagram only the height (length) of the bar represents the magnitude of the data; the width of the bar is unimportant. Since only one dimension carries meaning, a bar diagram is a one-dimensional diagram.

2. Data represented through a histogram can help in finding graphically the (i) mean (ii) mode (iii) median (iv) all the above

ANSWER (ii) mode. A histogram gives the value of the mode of a frequency distribution graphically — the x-coordinate of the dotted vertical line drawn through the tallest rectangle gives the mode.

3. Ogives can be helpful in locating graphically the (i) mode (ii) mean (iii) median (iv) none of the above

ANSWER (iii) median. The point where the ‘less than’ ogive and the ‘more than’ ogive intersect gives the median of the frequency distribution.

4. Data represented through arithmetic line graph help in understanding (i) long term trend (ii) cyclicity in data (iii) seasonality in data (iv) all the above

ANSWER (iv) all the above. An arithmetic line graph (time series graph) helps in understanding the long-term trend, cyclicity (periodicity) and seasonality in data over time.

5. Width of bars in a bar diagram need not be equal (True/False).

ANSWER False. In a bar diagram the bars are equi-width (and equi-spaced). Although the width itself is unimportant for comparison — only height matters — by convention all bars are drawn of equal width.

6. Width of rectangles in a histogram should essentially be equal (True/False).

ANSWER False. The width of a rectangle in a histogram equals the width of its class interval, and class intervals may be unequal. When widths differ, the heights are adjusted using frequency density so that the areas remain proportional to the frequencies.

7. Histogram can only be formed with continuous classification of data (True/False).

ANSWER True. A histogram is drawn only for a continuous variable. If the classes are not continuous, they must first be converted into continuous classes (exclusive form) before a histogram can be drawn.

8. Histogram and column diagram are the same method of presentation of data. (True/False)

ANSWER False. They are different. In a histogram no space is left between rectangles and it is drawn only for continuous variables, where area (not just height) is meaningful. In a column (bar) diagram, spaces are left between bars, it can be used for discrete and continuous data, and only the height matters.

9. Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)

ANSWER True. A histogram gives the mode graphically; the x-coordinate of the vertical line through the tallest rectangle (located by drawing diagonals at the peak) is the mode.

10. Median of a frequency distribution cannot be known from the ogives. (True/False)

ANSWER False. The median can be found from ogives — the point of intersection of the ‘less than’ and ‘more than’ ogives gives the median of the distribution.

11. What kind of diagrams are more effective in representing the following? (i) Monthly rainfall in a year (ii) Composition of the population of Delhi by religion (iii) Components of cost in a factory

ANSWER (i) Monthly rainfall in a year: a simple bar diagram is most effective — twelve equispaced bars (one per month) whose heights show the rainfall, allowing easy month-to-month comparison. (An arithmetic line graph can also show the trend across the year.) (ii) Composition of the population of Delhi by religion: a pie diagram is most effective, because it shows how the whole population is divided proportionally among the different religious communities as shares of one circle. (iii) Components of cost in a factory: a component (sub-divided) bar diagram or a pie diagram is most effective, since the total cost can be split into its component heads (raw material, labour, power, etc.) and each component compared as a part of the whole.

12. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form?

ANSWER The data (Census of India 2001, in crores) relate to workers and non-workers by location. To emphasise the share of non-workers and the level of urbanisation, present the figures as percentages rather than as raw numbers, because percentages make the comparison between rural and urban India direct. From the data: total population = 102 crore; rural = 74 crore and urban = 28 crore; rural non-workers = 43 crore and urban non-workers = 19 crore. Urbanisation = (28 ÷ 102) × 100 ≈ 27.5% (so about 72.5% of people live in rural areas — a low level of urbanisation). Share of non-workers within urban India = (19 ÷ 28) × 100 ≈ 67.9%, compared with (43 ÷ 74) × 100 ≈ 58.1% in rural India — clearly higher in towns and cities. A suitable table emphasising these points is given below.
LocationPopulation (crore)Share in total population (%)Non-workers (crore)Non-workers as % of that area
Rural7472.54358.1
Urban2827.51967.9
All India102100.06260.8
The percentage columns highlight both facts at a glance: urbanisation is low (only ~27.5% urban) while the proportion of non-workers is higher in urban India (~67.9%) than in rural India (~58.1%). Source: Census of India 2001.

13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?

ANSWER When the class intervals are equal, all rectangles have the same base (width), so the area of each rectangle is automatically proportional to its frequency. Hence the height of each rectangle can simply be taken equal to the frequency of that class, and the histogram is drawn directly. When the class intervals are unequal, taking the frequency as the height would distort the picture, because a wider class would get a larger area for the same frequency. In a histogram it is the area (not the height) that must be proportional to the frequency. So the heights are adjusted: for each class we compute the frequency density = class frequency ÷ class width, and plot frequency density (adjusted frequency) on the Y-axis instead of the raw frequency. This keeps the area of every rectangle proportional to its frequency and gives a correct histogram.

14. The Indian Sugar Mills Association reported that, ‘Sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off-take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’ (i) Present the data in tabular form. (ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why? (iii) Present these data diagrammatically.

ANSWER (i) Tabular form (figures in ‘000 tonnes, i.e. thousand tonnes), for the first fortnight of December:
Item2000 (‘000 tonnes)2001 (‘000 tonnes)
Production378387
Off-take: Internal consumption154283
Off-take: ExportsNil (0)41
Total off-take154324
Source: Indian Sugar Mills Association. (ii) Choice of diagram: a component (sub-divided) bar diagram is most suitable. Off-take has two components — internal consumption and exports — whose total can be shown as one bar split into parts. A component bar diagram for each year compares both the totals and the share of each component between 2000 and 2001 in a single picture. (Production can be shown as a separate simple bar alongside.) (iii) Diagram described in words: Take the years (2000, 2001) on the X-axis and quantity in ‘000 tonnes on the Y-axis (scale, say, 1 cm = 50 thousand tonnes). • 2000 off-take bar: a single bar of total height 154; the whole bar is ‘internal consumption’ (154) with no export segment (exports = 0). • 2001 off-take bar: a single bar of total height 324, divided into two segments — a lower segment of 283 for internal consumption and an upper segment of 41 for exports (283 + 41 = 324). The two bars (one beside the other), with the export segment shaded differently, immediately show that total off-take rose from 154 to 324 thousand tonnes and that exports (nil in 2000) appeared in 2001. Production can be added as two adjacent simple bars of heights 378 and 387.

15. The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.

YearAgriculture and allied sectorsIndustryServices
1994–955.09.27.0
1995–96–0.911.810.3
1996–979.66.07.1
1997–98–1.95.99.0
1998–997.24.08.3
1999–20000.86.98.2

Represent the data as multiple time series graphs.

ANSWER Multiple time series graph described in words: On the same pair of axes plot three line graphs — one each for Agriculture, Industry and Services. Take the years (1994–95 to 1999–2000) on the X-axis at equal spacing, and the growth rate (per cent) on the Y-axis. Because some agriculture values are negative, the Y-axis must extend from below 0 (about –2%) up to about 12% (suggested scale: 1 cm = 2%, with a clear zero line). Plot and join the points for each sector with a distinct line (different colour or line style, with a legend): • Agriculture and allied: 5.0 → –0.9 → 9.6 → –1.9 → 7.2 → 0.8. This line zig-zags sharply, even dipping below zero in 1995–96 and 1997–98, showing that agricultural growth is highly fluctuating (depends on the monsoon). • Industry: 9.2 → 11.8 → 6.0 → 5.9 → 4.0 → 6.9. This line starts high, peaks in 1995–96 and then falls and recovers slightly — a generally declining-then-stabilising trend. • Services: 7.0 → 10.3 → 7.1 → 9.0 → 8.3 → 8.2. This line stays comparatively high and stable (between about 7% and 10%) throughout the period. Interpretation: the three lines together show that the services sector grew most steadily and strongly, industry slowed down over the period, and agriculture was the most volatile, with negative growth in two years. This is exactly what a multiple time series (arithmetic line) graph is meant to reveal — comparative trends of several variables over time.

Extra Practice Questions

Short Answer Type Questions

Q1. What is textual presentation of data and when is it suitable?

ANSWERIn textual presentation, data are described within the running text of the report. It is suitable only when the quantity of data is small. Its drawback is that the entire text must be read to understand the data, though it allows the writer to emphasise particular points.

Q2. Distinguish between a caption and a stub in a table.

ANSWERA caption (column heading) is the designation given at the top of each column to explain the figures of that column, read vertically. A stub (row heading) is the designation given to each row, read horizontally; the complete left-hand column of stubs is called the stub column.

Q3. Convert a component of 25% into its angular component for a pie diagram.

ANSWERAngle = percentage × 3.6° = 25 × 3.6° = 90°. (A quarter of the circle, since 360° ÷ 4 = 90°.)

Q4. State two differences between a histogram and a bar diagram.

ANSWER(i) A histogram leaves no gap between rectangles, whereas a bar diagram keeps spaces between bars. (ii) A histogram is drawn only for continuous variables and its area is meaningful, whereas a bar diagram can show discrete or continuous data and only the height matters.

Q5. Why are pie charts drawn with percentage values rather than absolute values?

ANSWERA pie chart represents components as parts of one whole circle (treated as 100 parts of 3.6° each). The values of each category are first expressed as a percentage of the total and then converted into angles (percentage × 3.6°). Using percentages makes the components add up to exactly 100% (360°) and allows fair comparison of shares.

Long Answer Type Questions

Q1. Explain the four kinds of classification used in tabular presentation with one example each.

ANSWERTabulation may use four kinds of classification. Qualitative classification is done according to attributes such as sex, location or nationality — e.g. literacy classified by male/female and rural/urban. Quantitative classification is based on measurable characteristics such as age, income or height, using class limits — e.g. respondents grouped into age groups 20–30, 30–40, etc. Temporal classification takes time as the classifying variable (hours, days, months, years) — e.g. yearly sales of a tea shop from 1995 to 2000. Spatial classification is based on place — village, town, district, state or country — e.g. India’s exports classified by destination country. The right kind of classification makes a table organised and meaningful for further statistical analysis.

Q2. Describe the eight parts of a good statistical table.

ANSWERA good table has eight essential parts. (i) Table number identifies the table (whole numbers or subscripted numbers like 4.5). (ii) Title narrates the contents clearly and briefly, placed at the head. (iii) Captions (column headings) explain the figures of each column. (iv) Stubs (row headings) describe each row; the left column is the stub column. (v) Body is the main part containing the actual data, each figure fixed by its row and column. (vi) Unit of measurement is stated with the title (or with stubs/captions if units differ); large figures are rounded and the rounding method indicated. (vii) Source is a brief statement of where the data came from, given at the bottom. (viii) Note is the last part, explaining any special feature of the data not self-explanatory. Together these parts make the table complete, clear and unambiguous.

Q3. Compare and contrast the histogram, frequency polygon and ogive as ways of presenting a grouped frequency distribution.

ANSWERAll three are frequency diagrams for grouped data, but they differ in construction and use. A histogram is a set of adjacent rectangles with class intervals as bases and areas proportional to frequencies; it is drawn only for continuous variables and locates the mode graphically. A frequency polygon is obtained by joining the mid-points of the tops of the histogram’s rectangles with straight lines and closing it to the base line at both ends; it is the most common way of showing a grouped distribution and is convenient for comparing two or more distributions on the same axes. An ogive (cumulative frequency curve) plots cumulative frequencies against class limits — ‘less than’ against upper limits (never decreasing) and ‘more than’ against lower limits (never increasing); the intersection of the two ogives gives the median. Thus a histogram and polygon show the shape of the distribution and the mode, while ogives reveal cumulative position and the median.

MCQs & Assertion–Reason

1. Which of the following is NOT a form of presentation of data?

(a) Textual    (b) Tabular    (c) Diagrammatic    (d) Sampling

2. Classification of data according to time is called:

(a) qualitative    (b) quantitative    (c) temporal    (d) spatial

3. Classification on the basis of place is called:

(a) spatial    (b) temporal    (c) qualitative    (d) quantitative

4. The part of a table that contains the actual data is the:

(a) caption    (b) stub    (c) body    (d) title

5. To convert a percentage into the angle of a pie diagram, multiply it by:

(a) 3.6°    (b) 36°    (c) 1.8°    (d) 18°

6. A bar diagram divided into parts to show components of a total is a:

(a) simple bar diagram    (b) multiple bar diagram    (c) component bar diagram    (d) histogram

7. A histogram is drawn only for:

(a) discrete variables    (b) continuous variables    (c) attributes    (d) time series

8. In a ‘less than’ ogive, cumulative frequencies are plotted against the:

(a) lower class limits    (b) upper class limits    (c) class marks    (d) mid-values

9. Which diagram is best to show the proportional shares of a total (e.g. expenditure by head)?

(a) Histogram    (b) Ogive    (c) Pie diagram    (d) Frequency polygon

10. An arithmetic line graph is also called a:

(a) frequency curve    (b) time series graph    (c) component diagram    (d) pie chart

Answer key: 1-(d), 2-(c), 3-(a), 4-(c), 5-(a), 6-(c), 7-(b), 8-(b), 9-(c), 10-(b).

For each Assertion–Reason question, choose: (A) Both true and the Reason correctly explains the Assertion; (B) Both true but the Reason is not the correct explanation; (C) Assertion true, Reason false; (D) Assertion false, Reason true.

A-R 1. Assertion: Textual presentation is best suited for very large quantities of data.

Reason: In textual presentation the whole text must be read to comprehend the data.

A-R 2. Assertion: In a histogram with unequal class intervals, frequency density is plotted instead of frequency.

Reason: In a histogram the area of each rectangle must be proportional to the class frequency.

A-R 3. Assertion: A pie chart uses absolute values of components without converting them.

Reason: Each component’s percentage is multiplied by 3.6° to get its angle.

A-R 4. Assertion: The median of a frequency distribution can be located from the ogives.

Reason: The point of intersection of the ‘less than’ and ‘more than’ ogives gives the median.

A-R 5. Assertion: A histogram and a bar diagram are exactly the same.

Reason: A histogram leaves no gap between rectangles and is drawn only for continuous data, unlike a bar diagram.

Answer key: 1-(D), 2-(A), 3-(D), 4-(A), 5-(D).

Exam Tips & Common Mistakes

How to score full marks in this chapter

Remember the three forms of presentation (textual, tabular, diagrammatic) and the four kinds of classification (qualitative, quantitative, temporal, spatial). Memorise the eight parts of a table in order. For diagram questions, always state which diagram you would use and why: pie/component bar for shares of a whole, simple bar for category comparison, multiple bar/line for comparing sets over time, histogram/polygon/ogive for grouped frequency data. Keep the two key graphical results ready: histogram → mode and ogives intersection → median. When asked to draw, mention the axes, scale, and a legend.

Common mistakes to avoid

  • Calling a bar diagram “two-dimensional” — it is one-dimensional (only height matters).
  • Plotting raw frequency in a histogram with unequal class widths instead of frequency density.
  • Leaving gaps between rectangles in a histogram (gaps belong to bar diagrams only).
  • Using absolute values for a pie chart — convert to percentages, then to angles (percentage × 3.6°).
  • Confusing a ‘less than’ ogive (against upper limits) with a ‘more than’ ogive (against lower limits).
  • Saying a histogram gives the median or that ogives give the mode — it is the reverse.
  • Forgetting to give the table its number, title, unit, source and note.

Frequently Asked Questions

What is Chapter 4 of Class 11 Economics (Statistics for Economics) about?

Chapter 4, Presentation of Data, explains the three forms of presenting statistical data — textual, tabular and diagrammatic. It covers the four kinds of classification, the eight parts of a good statistical table, and diagrams such as bar diagrams, pie chart, histogram, frequency polygon, frequency curve, ogive and arithmetic line graph.

How do you find the mode and median graphically?

The mode of a frequency distribution is found graphically from a histogram — the x-coordinate of the vertical line through the tallest rectangle. The median is found from ogives — the point where the ‘less than’ and ‘more than’ ogives intersect gives the median.

How many questions are there in the NCERT Exercises of Chapter 4?

The end-of-chapter Exercises in Statistics for Economics Chapter 4 contain 15 questions: questions 1–10 are objective (multiple choice and True/False), and questions 11–15 are application questions involving choice of diagrams, tabulation and graphs. All are solved step by step on this page.

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