Page 285 - F2 - MA Integrated Workbook STUDENT 2018-19

Statistical techniques

 multi-item (or weighted) indices

– A weighted index measures the change in overall price or overall quantity
of a number of different items compared to the base year.

Example 8

The average prices of four commodities, along with the number of units used
annually by a company, are given in the following table:

Year 1 Year 2
Commodity Price per Price per Quantity
unit unit
$ $ Units

A 10 11 10

B 20 24 1
C 50 52 5
D 100 105 4

Calculate a weighted price index for year 2 based on year 1 using the
quantities given as weights.

Price index Quantity weighting Total Price index × Quantity

A 11/10 × 100 = 110 10 1,100

B 24/20 × 100 = 120 1 120

C 52/50 × 100 = 104 5 520

D 105/100 × 100 = 105 4 420

20 2,160

Weighted price index = 2,160/20 = 108

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