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Statistics · Class 12 Commerce

Ch 1Index Number — Class 12 Statistics, concept-first.

An index number is a statistical device that measures the average relative change in a group of related variables — such as prices, quantities, or values — over two different periods, one of which is treated as the base period and the other as the current period.

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Key concepts

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Tests of Adequacy — Time Reversal and Factor Reversal

The Time Reversal Test requires (as ratios) when the base and current years are interchanged; the Factor Reversal Test requires , the true value ratio.

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Chapter contents

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Meaning, Features and Uses of Index Numbers

An index number is a statistical device that measures the average relative change in a group of related variables — such as prices, quantities, or values — over two different periods, one of which is…

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Types of Index Numbers: Price, Quantity and Value

Index numbers are classified according to what they measure:

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Simple Index Numbers

When every commodity in a group is treated as equally important, the index constructed is called a simple (or unweighted) index number. There are two standard methods.

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Weighted Index Numbers: Laspeyres, Paasche and Fisher's Ideal

In real life, a family spends far more on food than on stationery, so a price rise in food should influence the overall index far more than an equal percentage rise in stationery.

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Tests of Adequacy: Time Reversal and Factor Reversal

Not every formula that "looks reasonable" is actually consistent. Statisticians test an index number formula against two conditions.

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Consumer Price Index (CPI) and Wholesale Price Index (WPI)

Two index numbers dominate real economic reporting in India, and Gujarat Std-12 Commerce Statistics students should be able to distinguish them clearly.

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Uses of Index Numbers: Deflating Money Wage and Income

The most powerful practical use of a price index in this chapter is deflating — separating a genuine change in purchasing power from a change that is purely due to price inflation.

Exercises

+Show 9 questions9 questions
  1. Q6Verify that Fisher's Ideal Index Number satisfies the Time Reversal Test, using the data of Commodities A, B, C, D from the worked examples…Free
  2. Q7Verify that Fisher's Ideal Index Number satisfies the Factor Reversal Test, for the same data.Free
  3. Q8Using value weights $w=p_0q_0$ for Commodities A, B, C, D (as in the earlier worked examples), calculate the Price Index by the Weighted Ave…Free
  4. Q9Using the base-year quantities $q_0$ (5, 4, 3, 2) and current-year quantities $q_1$ (6, 5, 4, 3) for Commodities A, B, C, D from the earlier…Preview
  5. Q10From the following group weights and price relatives, calculate the Consumer Price Index Number (Cost of Living Index) for the current year:…Preview
  6. Q11Which of the following index number formulae satisfies BOTH the Time Reversal Test and the Factor Reversal Test? (a) Laspeyres' Index (b) Pa…Preview
  7. Q12The money wage of a worker in the current year is Rs. 8,000 per month, and the Consumer Price Index (base year = 100) for the current year s…Preview
  8. Q13Mr. Patel's monthly salary rose from Rs. 6,000 to Rs. 9,000 over a period during which the Consumer Price Index rose from 100 to 160. Has hi…Preview
  9. Q14Distinguish between the Consumer Price Index (CPI) and the Wholesale Price Index (WPI).Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 31 questions31 questions
  1. Q1If the purchasing power of money is 0.75 in the year 2019 with respect to the base year 2018 then what will be the price index number for th…Preview
  2. Q2State the main difference between fixed base method and chain base method.Preview
  3. Q3The percentage increase in the price relatives of 3 items $A$, $B$, and $C$ are $315$, $328$ and $390$ respectively. If the importance of th…Preview
  4. Q4Compute the cost of living index number by the method of total expenditure from the following data for the year 2019: | Items | A | B | C |…Preview
  5. Q5Compute the Laspeyre's, Paasche's and Fisher's index numbers for the year 2019 from the data given below: | Items | Quantity Year 2018 | Qua…Preview
  6. Q6The price of an item increased by 4.5 times in the current year as compared to the base year. What will be the price index number? (a) 45 (b…Preview
  7. Q7If the purchasing power of money is 0.75 in the year 2021 with respect to the base year 2020 then what will be the price index number for th…Preview
  8. Q8Name the important basic tests of index numbers.Preview
  9. Q9The wholesale price index numbers of the year 2020 and 2021 are found to be 150.2 and 165.7 respectively. Find the rate of inflation using i…Preview
  10. Q10The details of expenditure on clothing for the worker class of a region are as follows. Find the index number for clothing by Family Budget…Preview
  11. Q11Calculate the real wages of a worker class from the following data about their monthly wages. | Year | 2016 | 2017 | 2018 | 2019 | 2020 | 20…Preview
  12. Q12Compute Laspeyre's, Paasche's and Fisher's index number for the year 2021 from the data given below. | Item | Quantity Year 2021 | Quantity…Preview
  13. Q13Which index number is used to find the rate of inflation? (a) (A) Cost of Living Index Number (b) (B) Wholesale Price Index Number (c) (C) I…Preview
  14. Q14State the two popular methods of assigning explicit weight.Preview
  15. Q15If the average disposable income of family of a class is ₹25000 in the year 2017 and if the cost of living index number of that class for th…Preview
  16. Q16The data about per unit price and weights for four different items in the year 2017 and 2018 are as follows. Compute the index number of the…Preview
  17. Q17Compute the Laspeyre's, Paasche's and Fisher's Index numbers for the year 2019 from the data given below: | Items | Quantity Year 2018 | Qua…Preview
  18. Q18Which prices are considered in the construction of the cost of living index number? (a) Market price (b) Wholesale price (c) Average price (…Preview
  19. Q19If the purchase power of money is 0.75 in the year 2024 with respect to the base year 2023 then what will be the price index number for the…Preview
  20. Q20Write the formula to find the rate of inflation.Preview
  21. Q21The cost of living index numbers and average monthly wage from the year 2020 to 2023 are given as follows. Find the real wage for each year…Preview
  22. Q22The chain base index numbers of sales of a certain type of scooter from the year 2020 to 2024 are as follows. Find fixed base index numbers…Preview
  23. Q23The prices of three items among five fuel items were increased by 50%, 90% and 110% in the year 2024 as compared to the base year 2023. The…Preview
  24. Q24Find Laspeyre's, Paasche's and Fisher's index numbers for the year 2024 with base year 2023 from the data about price and consumption of foo…Preview
  25. Q25Which expenditure of items is assigned as weights in the method of family budget? (a) Expenditure of selected year (b) Average annual expend…Preview
  26. Q26If $I_P = I_F$, which of the following statements is true? (a) $I_P = 2I_L$ (b) $I_F = \dfrac{I_L}{2}$ (c) $I_F = I_P = I_L$ (d) $4I_F = I_L…Preview
  27. Q27Write the formula to find Real wage.Preview
  28. Q28If the cost of living index number of the current year has increased to 180 from the base year index number 100 and if the average income of…Preview
  29. Q29The chain base index numbers of agricultural production of a state from the year 2008-2013 are as follows. Compute the fixed base index numb…Preview
  30. Q30The information about six different items used in the furniture items is as follows. Find the index number for the year 2015 with the base y…Preview
  31. Q31Find Fisher's index number for the year 2015 by taking the year 2014 as the base year from the data given below about consumption and total…Preview

More questions

+Show 5 questions5 questions
  1. Example 1From the following data, calculate the Simple Aggregative Price Index Number for the current year, taking the earlier year as base: | Commod…Free
  2. Example 2Using the same base-year and current-year prices as above, calculate the Price Index Number by the Simple Average of Price Relatives method.Free
  3. Example 3From the following data, calculate Laspeyres' Price Index Number: | Commodity | $p_0$ | $p_1$ | $q_0$ | |---|---|---|---| | A | 10 | 12 | 5…Preview
  4. Example 4Continuing the same commodities, with current-year quantities $q_1$: A = 6, B = 5, C = 4, D = 3, calculate Paasche's Price Index Number.Preview
  5. Example 5Using Laspeyres' Index (115.67) and Paasche's Index (115.25) obtained above, calculate Fisher's Ideal Index Number.Preview