Class | Subject | Book | Chapter | Session | Questions covered |
|---|---|---|---|---|---|
XI | Economics | Statistics for Economics (NCERT) | 4 – Presentation of Data | 2026-27 | 15 of 15 |
Chapter at a glance
Topic | Key facts |
|---|---|
Forms | Textual, tabular and diagrammatic presentation |
Table parts | Table number, title, captions (column heads), stubs (row heads), body, unit of measurement, source, note |
Geometric diagrams | Bar diagrams (simple, multiple, component), pie diagram |
Frequency diagrams | Histogram, frequency polygon, frequency curve, ogive |
Arithmetic line graph | Time series graph; shows trend, cycles and seasonality |
Graphical location | Histogram → mode; ogives → median |
Exercise Questions
Bar diagram is a
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- one-dimensional diagram (ii) two-dimensional diagram (iii) diagram with no dimension (iv) none of the above
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Only the length (height) of a bar matters; the width is uniform and carries no meaning.
- one-dimensional diagram
Data represented through a histogram can help in finding graphically the
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- mean (ii) mode (iii) median (iv) all the above
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The mode is found from the highest rectangle of a histogram by joining its corners to the adjacent rectangles.
- mode
Ogives can be helpful in locating graphically the
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- mode (ii) mean (iii) median (iv) none of the above
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The point where the “less than” and “more than” ogives intersect gives the median (it can also be read at N/2 on one ogive).
- median
Data represented through arithmetic line graph help in understanding
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- long term trend (ii) cyclicity in data (iii) seasonality in data (iv) all the above
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A time-series line graph shows trend, cyclical and seasonal movements.
- all the above
Width of bars in a bar diagram need not be equal (True/False).
Answer
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False. In a bar diagram all bars must have equal width and equal spacing; only their heights represent values.
False
Width of rectangles in a histogram should essentially be equal (True/False).
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False. The width of each rectangle equals the class interval, which may be unequal; with unequal classes the heights are adjusted (frequency density) so that areas remain proportional to frequencies.
False
Histogram can only be formed with continuous classification of data (True/False).
Answer
Answer
True. A histogram is drawn for a continuous (exclusive) classification; rectangles are adjacent without gaps. Inclusive classes must first be converted to continuous form.
True
Histogram and column diagram are the same method of presentation of data. (True/False)
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Answer
False. A column (bar) diagram is one-dimensional with equal-width bars separated by gaps, used for discrete or categorical data. A histogram is two-dimensional (area matters), with adjacent rectangles for a continuous frequency distribution.
False
Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)
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Answer
True
Median of a frequency distribution cannot be known from the ogives. (True/False)
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False. The median can be located from ogives (intersection of the less-than and more-than ogives, or reading the value at N/2).
False
What kind of diagrams are more effective in representing the following?
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- 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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- Monthly rainfall in a year: a simple bar diagram (or an arithmetic line graph), since it shows values of one variable over 12 months.
- Composition of population of Delhi by religion: a pie diagram (or component bar diagram), since it shows the parts of a whole.
- Components of cost in a factory: a pie diagram or component (sub-divided) bar diagram, since it shows the share of each cost item in total cost.
- Bar diagram / line graph (ii) Pie diagram (iii) Pie diagram or component bar diagram
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 in the text (Census 2001, Case 2) can be tabulated with percentage columns that bring out the two points:
Table: Population of India by residence and working status, 2001 (in crore)
Residence | Workers | Non-workers | Total | Non-workers (% of total) | Share in total population (%) |
|---|---|---|---|---|---|
Rural | 31 | 43 | 74 | 58.1 | 72.5 |
Urban | 9 | 19 | 28 | 67.9 | 27.5 |
Total | 40 | 62 | 102 | 60.8 | 100 |
Source: Census of India 2001.
- The column “Non-workers (% of total)” emphasises that urban areas have a higher share of non-workers (67.9 %) than rural areas (58.1 %).
- The column “Share in total population” emphasises the low level of urbanisation: only 27.5 % of people live in towns.
These columns can be printed in bold or placed next to the stub for emphasis.
Add percentage columns: non-workers as % of each area’s population (urban 67.9 % vs rural 58.1 %) and each area’s share of total population (urban only 27.5 %).
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
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- Equal class intervals: all rectangles have the same width, so their heights are simply the frequencies.
- Unequal class intervals: the area of each rectangle must be proportional to its frequency, so the frequencies must be adjusted. We compute frequency density (frequency ÷ class width), or adjust frequencies to a standard (usually the lowest) class width:
The rectangles are drawn with heights equal to the adjusted frequencies (or densities) and widths equal to their class intervals.
With equal intervals heights equal frequencies; with unequal intervals frequencies are first adjusted (frequency density) so that areas remain proportional to frequencies.
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.’
Answer
- Present the data in tabular form.
- Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why?
- Present these data diagrammatically.
Answer
(i) Tabular form
Table: Production and off-take of sugar, first fortnight of December (in thousand tonnes)
Item | December 2000 | December 2001 |
|---|---|---|
Production | 378 | 387 |
Off-take for internal consumption | 154 | 283 |
Off-take for exports | 0 | 41 |
Total off-take | 154 | 324 |
Source: Indian Sugar Mills Association.
(ii) Choice of diagram. A multiple (grouped) bar diagram is most suitable, because we have to compare the same items (production, internal off-take, exports) for two years side by side.
(iii) Diagram
Tabulate the three items for 2000 and 2001; a multiple bar diagram best compares them year-wise (shown above).
The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.
Answer
Year | Agriculture and allied sectors | Industry | Services |
|---|---|---|---|
1994–95 | 5.0 | 9.2 | 7.0 |
1995–96 | –0.9 | 11.8 | 10.3 |
1996–97 | 9.6 | 6.0 | 7.1 |
1997–98 | –1.9 | 5.9 | 9.0 |
1998–99 | 7.2 | 4.0 | 8.3 |
1999–2000 | 0.8 | 6.9 | 8.2 |
Represent the data as multiple time series graphs.
Answer
Years are taken on the X-axis and growth rates (%) on the Y-axis; each sector is plotted as a separate line on the same graph. Since agriculture has negative values, the X-axis is drawn at 0 with negative values below it.
Interpretation: agricultural growth fluctuates sharply (even negative in 1995–96 and 1997–98) because it depends on the monsoon; industrial growth rose in 1995–96 and then slowed; services grew steadily at about 7–10 %, the most stable sector.
Plot three lines (agriculture, industry, services) against years on one graph; agriculture is most volatile and services most stable.
Topic checklist
- Textual, tabular and diagrammatic presentation
- Parts of a table and kinds of classification
- Bar diagrams and pie diagram
- Histogram (equal and unequal classes), frequency polygon, ogives
- Arithmetic line graphs (time series)