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Questions
Explain the steps involved in the construction of index numbers.
Define Index number and explain the various steps involved in the construction of index numbers
Solution
Index numbers are one of the most used statistical tools in economics. An index number is a device to measure changes in an economic variable (or group of variables) over a period of time.
The following steps are involved in the construction of index numbers:
- Purpose of index number: The purpose for constructing the index number, its scope as well as which variable is intended to be measured should be clearly decided to achieve fruitful results.
- Selection of the base year: The base year is also called the reference year. It is the year against which comparisons are made. The base year should be normal i.e. it should be free from natural calamities. It should not be too distant from the past.
- Selection of items: It is necessary to select a sample of the number of items to be included in the construction of a particular index number. For example, in the construction of price index numbers, it is impossible to include each and every commodity. The commodities to be selected should represent the tastes, habits, and customs of the people. Besides this, only standardized or graded items should be included to give better results.
- Selection of price quotations: Prices of the selected commodities may vary from place to place and shop to shop in the same market. Therefore, it is desirable that price quotations should be obtained from an unbiased price reporting agency. To achieve accuracy, a proper selection of representative places and persons is required.
- Choice of a suitable average: The construction of index numbers requires the choice of a suitable average. Generally, the Arithmetic mean is used in the construction of index numbers because it is simple to compute compared to other averages.
- Assigning proper weights: Weight refers to the relative importance of the different items in the construction of an index number. Weights are of two types i.e. quantity weights (q) and value weights (p × q). Since all items are not of equal importance, by assigning specific weights, better results can be achieved.
- Selection of an appropriate formula: Various formulae are devised for the construction of index numbers. The choice of a suitable formula depends upon the purpose of the index number and the availability of data.
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RELATED QUESTIONS
Laaspeyre's index : _________ :: Paasche's index : Current year quantities
Calculate the price index number from the given data:
Commodity | A | B | C | D |
Price in 2005 (₹) | 6 | 16 | 24 | 4 |
Price in 2010 (₹) | 8 | 18 | 28 | 6 |
Solve the following:
Calculate Quantity Index number from the given data:
Commodity | P | Q | R | S | T |
Base year quantities | 170 | 150 | 100 | 195 | 205 |
Current year quantities | 90 | 70 | 75 | 150 | 95 |
Solve the following:
Calculate Value Index number from the given data:
Commodity | Base year | Current year | ||
Price | Quantity | Price | Quantity | |
A | 40 | 15 | 70 | 20 |
B | 10 | 12 | 60 | 22 |
C | 50 | 10 | 90 | 18 |
D | 20 | 14 | 100 | 16 |
E | 30 | 13 | 40 | 15 |
Calculate Laaspeyre's index from the given data:
Commodity | Base year | Current year | ||
Price | Quantity | Price | Quantity | |
X | 8 | 30 | 12 | 25 |
Y | 10 | 42 | 20 | 16 |
Solve the following:
Calculate Paasche's index from the given data:
Commodity | Base year | current year | ||
Price | Quantity | Price | Quantity | |
X | 8 | 30 | 12 | 25 |
Y | 10 | 42 | 20 | 16 |
Find the Price Index Number using Simple Aggregate Method in the following example.
Use 1995 as base year in the following problem.
Commodity | P | Q | R | S | T |
Price (in ₹) in 1995 | 15 | 20 | 24 | 23 | 28 |
Price (in ₹) in 2000 | 27 | 38 | 32 | 40 | 45 |
Find the Price Index Number using Simple Aggregate Method in the following example.
Use 1995 as base year in the following problem.
Commodity | A | B | C | D | E |
Price (in ₹) in 1995 | 42 | 30 | 54 | 70 | 120 |
Price (in ₹) in 2005 | 60 | 55 | 74 | 110 | 140 |
Find the Price Index Number using Simple Aggregate Method in the following example.
Commodity | Unit | Base Year Price (in ₹) | Current Year Price (in ₹) |
Wheat | kg | 28 | 36 |
Rice | kg | 40 | 56 |
Milk | litre | 35 | 45 |
Clothing | meter | 82 | 104 |
Fuel | litre | 58 | 72 |
Find the Price Index Number using the Simple Aggregate Method in the following example.
Use 2000 as base year in the following problem.
Commodity | Price (in ₹) for year 2000 |
Price (in ₹) for year 2006 |
Watch | 900 | 1475 |
Shoes | 1760 | 2300 |
Sunglasses | 600 | 1040 |
Mobile | 4500 | 8500 |
Find the Price Index Number using the Simple Aggregate Method in the following example.
Use 1990 as base year in the following problem.
Commodity | Unit | Price (in ₹) for year 2000 |
Price (in ₹) for year 2006 |
Butter | kg | 27 | 33 |
Cheese | kg | 30 | 36 |
Milk | litre | 25 | 29 |
Bread | loaf | 10 | 14 |
Eggs | doz | 24 | 36 |
Ghee | tin | 250 | 320 |
Find the Price Index Number using the Simple Aggregate Method in the following example.
Assume 2000 to be base year in the following problem.
Fruit | Unit | Price (in ₹) in 2000 |
Price (in ₹) for 2007 |
Mango | doz | 250 | 300 |
Banana | doz | 12 | 24 |
Apple | kg | 80 | 110 |
Peach | kg | 75 | 90 |
Orange | doz | 36 | 65 |
Sweet Lime | doz | 30 | 45 |
Find the Price Index Number using the Simple Aggregate Method in the following example.
Use 2005 as base year in the following problem.
Vegetable | Unit | Price (in ₹) in 2005 |
Price (in ₹) for 2012 |
Ladies Finger | kg | 32 | 38 |
Capsicum | kg | 30 | 36 |
Brinjal | kg | 40 | 60 |
Tomato | kg | 40 | 62 |
Potato | kg | 16 | 28 |
Find the Quantity Index Number using the Simple Aggregate Method in the following example.
Commodity | I | II | III | IV | V |
Base Year Quantities | 140 | 120 | 100 | 200 | 225 |
Current Year Quantities | 100 | 80 | 70 | 150 | 185 |
Find the Quantity Index Number using the Simple Aggregate Method in the following example.
Commodity | A | B | C | D | E |
Base Year Quantities | 360 | 280 | 340 | 160 | 260 |
Current Year Quantities | 440 | 320 | 470 | 210 | 300 |
Find the Value Index Number using Simple Aggregate Method in the following example.
Commodity | Base Year | Current Year | ||
Price | Quantity | Price | Quantity | |
A | 50 | 22 | 70 | 14 |
B | 70 | 16 | 90 | 22 |
C | 60 | 18 | 105 | 14 |
D | 120 | 12 | 140 | 15 |
E | 100 | 22 | 155 | 28 |
Find x if the Price Index Number by Simple Aggregate Method is 125.
Commodity | P | Q | R | S | T |
Base Year Price (in ₹) | 8 | 12 | 16 | 22 | 18 |
Current Year Price (in ₹) |
12 | 18 | x | 28 | 22 |
Find x if the Price Index Number by Simple Aggregate Method is 120, taking 1995 as base year.
Commodity | A | B | C | D |
Price (in ₹) for 1995 | 95 | y | 80 | 35 |
Price (in ₹) for 2003 | 116 | 74 | 92 | 42 |
Statements related to weighted index number:
- Suitable weights are assigned to various commodities.
- It gives relative importance to the commodity in the group.
- In most cases, quantities are used as weights.
- Laaspeyre’s Price index and Paasche’s Price Index are methods of constructing weighted index number.
Find the odd word
Steps involved in the construction of index number -
Assertion (A): Generally, arithmetic mean is used in the construction of index numbers.
Reasoning (R): Arithmetic mean is simple to compute compared to other averages.
State with reason whether you agree or disagree with the following statement:
Any year can be selected as the base year
Study the following table, figure, passage and answer the question given below it.
Commodities | Price in 2015 in Rs (base year) P0 |
Price in 2019 in Rs. (current year) P1 |
L | 20 | 30 |
M | 60 | 80 |
N | 100 | 130 |
O | 40 | 60 |
Total | ∑P0 = ? | ∑P1 = ? |
- Complete the above table (1m)
- Construct Price Index number from the above data (3m)
State with reasons whether you agree or disagree with the following statement:
It is not essential to decide the purpose of an index number while constructing it.
Explain the steps in constructing a price index number.