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NCERT · Class 11 · Statistics

Chapter 7: Index Numbers

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

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Textbook exercises

22 questions
Q1Multiple choice

An index number which accounts for the relative importance of the items is known as

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Correct option: A
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Worked solution
ANSWER (i) weighted index. A weighted index assigns weights to items in proportion to their relative importance (such as the share of expenditure), so that more important items influence the index more.
Q2Multiple choice

In most of the weighted index numbers the weight pertains to

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Correct option: A
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Worked solution
ANSWER (i) base year. Base-year weights are generally preferred because calculating fresh weights every year is inconvenient, and base-year weights keep the basket fixed and comparable (this is the basis of Laspeyre’s index).
Q3Multiple choice

The impact of change in the price of a commodity with little weight in the index will be

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Correct option: A
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Worked solution
ANSWER (i) small. Since the contribution of an item to a weighted index is proportional to its weight, a price change in a low-weight commodity has only a small effect on the overall index.
Q4Multiple choice

A consumer price index measures changes in

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Correct option: A
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Worked solution
ANSWER (i) retail prices. The CPI (cost-of-living index) reflects the prices actually paid by consumers at the retail level for a typical basket of goods and services.
Q5Multiple choice

The item having the highest weight in consumer price index for industrial workers is

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Correct option: A
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ANSWER (i) Food. Food and beverages occupy the largest proportion of a worker’s expenditure, so this group carries the highest weight in the CPI for industrial workers.
Q6Multiple choice

In general, inflation is calculated by using

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Correct option: A
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ANSWER (i) wholesale price index. In India the WPI is widely used to measure the rate of inflation, as it captures the general change in price level and the data are available quickly.
Q7Written answer

Why do we need an index number?

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Worked solution
ANSWER When many related variables change at different rates, describing each change separately is confusing. An index number condenses all these changes into a single comparable figure, showing the average change between two periods. Index numbers are indispensable in practice: the WPI and CPI measure inflation and the cost of living; the CPI helps calculate real wages and the purchasing power of money and is used in wage negotiation, income, price and rent policy and taxation; the IIP shows changes in industrial output; the agricultural production index tracks farm performance; and the Sensex guides investors. They are therefore essential tools in economic analysis and policy making.
Q8Written answer

What are the desirable properties of the base period?

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Worked solution
ANSWER The base period should be a normal year — free from abnormal events such as war, famine, boom, slump, earthquake or major political upheaval — so that it does not contain extreme values. It should not be too far in the past, because old baskets become unrepresentative (many items in a 1960 basket no longer exist); a comparison of 1993 with 2005 is more meaningful than 1960 with 2005. The base period should also be of a suitable length and the base must be updated routinely to keep the index relevant.
Q9Written answer

Why is it essential to have different CPI for different categories of consumers?

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Worked solution
ANSWER Different groups of consumers have different consumption baskets and spending patterns, so the same price change affects them differently. For instance, a rise in the petrol price hardly touches a poor agricultural labourer, but it matters to urban commuters. Because the items and their weights differ from group to group, a single index cannot fairly represent everyone. Hence separate CPIs are prepared — for industrial workers, agricultural labourers, rural labourers, and urban consumers — so that each measures the cost-of-living change for that category accurately.
Q10Written answer

What does a consumer price index for industrial workers measure?

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Worked solution
ANSWER The CPI for industrial workers measures the average change in the retail prices of a fixed basket of goods and services typically consumed by industrial workers, relative to a base year (base 2001 = 100). For example, a CPI(IW) of 277 in December 2014 means a worker who spent Rs 100 on that basket in 2001 needed Rs 277 in December 2014 to buy the same basket — it tracks the change in their cost of living.