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Calculate Walsh’s Price Index Number. Commodity Base Year Current Year Price Quantity Price Quantity L 4 16 3 19 M 6 16 8 14 N 8 28 7 32 - Mathematics and Statistics

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Question

Calculate Walsh’s Price Index Number.

Commodity Base Year Current Year
Price Quantity Price Quantity
L 4 16 3 19
M 6 16 8 14
N 8 28 7 32
Sum
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Solution

Walsh’s Price Index = `(sum(P_1 xx sqrt(q_0q_1)))/(sum(P_0 xx sqrt(q_0q_1))) xx 100` 

For Commodity L:

P0​ = 4, q0 = 16, P1 ​= 3, q1 = 19

`sqrt(16xx19) = sqrt304 = 17.44`

`P_1 xx sqrt(q_0q_1) = 3 xx 17.44 = 52.32`

P0 ​× `sqrt(q_0​q_1)` ​​= 4 × 17.44 = 69.76

For Commodity M:

P0​ = 6, q0 = 16, P1 = 8, q1 = 14

`sqrt(16xx14) = sqrt224 = 14.97`

P1 ​× `sqrt(q_0​q_1)`​​ = 8 × 14.97 = 119.76

P0​ × `sqrt(q_0​q_1)` ​​= 6 × 14.97 = 89.82

For Commodity N:

P0 = 8, q0 = 28, P1 = 7, q1 = 32

`sqrt(28xx32) = sqrt896 = 29.93`

P1 × `sqrtq_0q_1` = 7 × 29.93 = 209.51

P0​ × `sqrt(q_0q_1)` = 8 × 29.93 = 239.44

Totals:

`sum P_1sqrt(q_0q_1)` = 52.32 + 119.76 + 209.51 = 381.59

`sum P_0sqrt(q_0q_1)` = 69.76 + 89.82 + 239.44 = 398.99

`= 381.59/398.99 = 100`

= 95.64

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Construction of Index Numbers - Weighted Aggregate Method
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Chapter 5: Index Numbers - Exercise 5.2 [Page 82]

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