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Mathematics and Statistics · Class 12 Commerce

Ch 13Index Numbers — Class 12 Mathematics and Statistics, concept-first.

Prices, production, wages and the cost of living do not stay fixed — they rise and fall from year to year. To describe such a change in a group of related items by a single figure, statisticians use an index number.

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Key concepts

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Simple Aggregate Method

The Simple Aggregate Method builds a price index by adding the base-year prices of all included commodities to get , adding their current-year prices to get , and computing .

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Chapter contents

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Meaning, Features and Uses of Index Numbers

Prices, production, wages and the cost of living do not stay fixed — they rise and fall from year to year.

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Simple (Unweighted) Aggregate Method

The most direct way to build a price index for a group of commodities is the simple aggregate method. We total the current-year prices of all commodities, total their base-year prices, and express the…

3

Weighted Aggregate Methods

The simple aggregate index treats every commodity alike. In reality a household spends far more on rice than on, say, matchboxes, so price changes should be weighted by the quantities consumed.

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Cost of Living Index Number

A cost of living index number (CLI), also called a consumer price index, measures the change in the general level of prices of the goods and services a particular class of people (e.g.

Exercises

+Show 7 questions7 questions
  1. Q9Find the price index number for the current year by the simple aggregate method. | Commodity | $p_0$ (₹) | $p_1$ (₹) | |---|---|---| | P | 2…Free
  2. Q10Compute Laspeyre's and Paasche's price index numbers for the following data. | Commodity | $p_0$ | $q_0$ | $p_1$ | $q_1$ | |---|---|---|---|…Free
  3. Q11Calculate Fisher's ideal price index number for the data below. | Commodity | $p_0$ | $q_0$ | $p_1$ | $q_1$ | |---|---|---|---|---| | A | 10…Free
  4. Q12Find the cost of living index number by the family budget method. | Group | $p_0$ (₹) | $p_1$ (₹) | Weight $W$ | |---|---|---|---| | Food |…Preview
  5. Q13Fisher's ideal price index number is the ______ of Laspeyre's and Paasche's index numbers. (a) arithmetic mean (b) geometric mean (c) harmon…Preview
  6. Q14Which quantities are used as weights in Laspeyre's price index number? (a) current-year quantities $q_1$ (b) base-year quantities $q_0$ (c)…Preview
  7. Q15Distinguish between Laspeyre's and Paasche's price index numbers, and state one advantage of Fisher's ideal index over both.Preview

Sample & Board Papers

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

+Show 20 questions20 questions
  1. Q1Choose the correct alternative : The price Index Number by Weighted Aggregate Method is given by ______. (a) $\dfrac{\sum p_1 w}{p_0 w} \tim…Preview
  2. Q2State whether the following statement is true or false: Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's…Preview
  3. Q3If $P_{01}(L) = 121$, $P_{01}(P) = 100$, then $P_{01}(F) =$ ______.Preview
  4. Q4Calculate the cost of living index number for the following data by aggregative expenditure method: | Group | Base year | Current year | | |…Preview
  5. Q5Quantity Index Number by Weighted Aggregate Method is given by ______. (a) $\sum \frac{q_1 w}{q_0 w} \times 100$ (b) $\sum \frac{q_0 w}{q_1…Preview
  6. Q6Laspeyre’s Price Index Number uses current year’s quantities as weights. (a) True (b) FalsePreview
  7. Q7Walsh’s Price Index Number is given by _______.Preview
  8. Q8Calculate Marshall – Edgeworth’s price index number for the following data: | Commodity | Base year | Current year | | | | --- | --- | --- |…Preview
  9. Q9Dorbish-Bowley’s Price Index Number is given by ______. (a) $\dfrac{\dfrac{\sum p_1 q_0}{\sum p_0 q_1} + \dfrac{\sum p_0 q_1}{\sum p_1 q_0}}…Preview
  10. Q10$\displaystyle\sum \dfrac{p_0 q_0}{p_1 q_1} \times 100$ is Value Index Number by Simple Aggregate Method. (a) True (b) FalsePreview
  11. Q11The cost of living index number using Weighted Relative Method is given by ______.Preview
  12. Q12Solve the following problem: If find $x$ is Walsh’s Price Index Number is 150 for the following data | Commodity | Base Year | Current Year…Preview
  13. Q13If $P_{01}(L) = 90$ and $P_{01}(P) = 40$, then $P_{01}(D - B)$ is ______. (a) 65 (b) 50 (c) 25 (d) 130Preview
  14. Q14Cost of living index number is used in calculating purchasing power of money. (a) True (b) FalsePreview
  15. Q15Quantity Index Number by Weighted Aggregate Method is given by ______.Preview
  16. Q16Find x if the cost of living index is 150. | Group | Food | Clothing | Fuel & Lighting | House Rent | Miscellaneous | | --- | --- | --- | --…Preview
  17. Q17Price Index Number by Simple Aggregate Method is given by ______. (a) $\sum \frac{p_1}{p_0} \times 100$ (b) $\sum \frac{p_0}{p_1} \times 100…Preview
  18. Q18The cost of living Index Number using weighted relative method is given by $\frac{\sum IW}{\sum W}$.Preview
  19. Q19If $P_{01}(L) = 225$, $P_{01}(P) = 144$ then $P_{01}(F)$ = ______.Preview
  20. Q20Calculate (a) Laspeyre’s and (b) Paasche's Price Index Numbers for the following data: | Commodity | Base year | Current year | | | | --- |…Preview

More questions

+Show 8 questions8 questions
  1. Example 1Define an index number and state any four important uses of index numbers.Free
  2. Example 2Construct the price index number for the current year by the simple aggregate method. | Commodity | Base-year price $p_0$ (₹) | Current-year…Free
  3. Example 3For the data below, compute (a) Laspeyre's and (b) Paasche's price index numbers. | Commodity | $p_0$ | $q_0$ | $p_1$ | $q_1$ | |---|---|---…Free
  4. Example 4Using the same data as the previous example ($\sum p_0q_0=170,\ \sum p_1q_0=216,\ \sum p_0q_1=190,\ \sum p_1q_1=237$), compute Fisher's idea…Preview
  5. Example 5For the same data ($\sum p_0q_0=170,\ \sum p_1q_0=216,\ \sum p_0q_1=190,\ \sum p_1q_1=237$), compute (a) the Marshall–Edgeworth price index…Preview
  6. Example 6Calculate the cost of living index number for the current year by the aggregate expenditure method. | Commodity | $p_0$ (₹) | $q_0$ | $p_1$…Preview
  7. Example 7Compute the cost of living index number by the family budget method. | Group | Base price $p_0$ (₹) | Current price $p_1$ (₹) | Weight $W$ |…Preview
  8. Example 8The cost of living index number for a certain year is 250 (base year = 100). (i) A worker earned ₹6,000 in the base year; what salary would…Preview