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NCERT · Class 11 · Statistics

Chapter 4: Presentation of Data

Practice each question, then open the answer or worked solution.

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Textbook exercises

15 questions
Q11Written answer

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

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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.
Q12Written answer

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?

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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.
Q13Written answer

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

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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.
Q14Written answer

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.

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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.
Q15Written answer

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.

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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.