MT_F4_10 Index Numbers_3

10.2 Composite Index ( I )

I   IW - I read as i bar
W
-  : Summation 总和
I = price index or index number
W = weightage - IW : (price index 乘 weightage)

重量/成分

- Weightage ： the value of the

weightage shows the important of the
item, it can be in the form of numbers,
ratio, percentage, …..

Example：Calculate the composite index for each of the following:

(a) Item Price index Weightage I   IW
W
P 120 3
Q 160 5  120(3) 160(5) 145(4)
R 145 4 354

 145

(b) Table 1 shows the expenditure of utility index of a factory in the year 2018
based on the year 2013. The pie chart shows the percentages of the usage in a
month.

Utility Weightage Fuel Electric
25% 58%
Fuel 125
Water 135 Water
Electricity 140 17%

I   IW
W

 125(25) 135(17) 140(58)
25 17  58

 135.4

(c) Table 2 shows the price indices and the weightages of four items, P, Q. R and
S in year 2015 based on 2012. Calculate the composite index of all the items in
year 2015 based on 2012.

Item Price index Weightage

P 110 3 110
Q 105 4
R 120 1
S 115 2

(d) Table 3 shows the price indices and weightages of 3 items, X, Y and Z in year
2018 based on 2016. Calculate the composite index of all the items in year
2018 based on 2016.

Item X YZ 97
Index number 91 102 95
Weightage 2 44

(e) Table 4 shows the price indices and the percentages of usage for four
ingredients in the making of a kind of dessert.

Ingredient Price index in the year 2019 Percentage (%)
based on year 2016
P
Q 160 30
R
S 150 10

125 20

135 40

Calculate the composite index for the cost of making the dessert in the year
2019 based on year 2016.

142

(f) Calculate the composite index:

Item A B C
Price in 2015 (RM) 2.50 1.20 5.00

Price in 2019 (RM) 3.00 4.80 5.70

Weightage 1 32

 item A I19  P19 100 这题要求找 Composite index，
P15 但 是 题 目 没 有 提 供 price
index，我们就要用 formula 找
 3.00 100 出三样产品的 price index。
2.50
I  P1 100
 120 P0

 item B I19  4.80 100
1.20

 400

 item C I19  5.70 100
5.00

 114

I  120(1)  400(3)  114(2)
13 2

 258

(g) Table 5 shows the price of five types of goods in the year 2005 and 2006 with
their corresponding weightages, Calculate the composite index in year 2006
based on 2005.

Goods Price (RM) Price (RM) Weightage
2005 2006
P 5 6 1
Q 20 23 2
R 8 12 3
S 16 18 4
T 10 13 5

126.7

(h) Table 6 shows the price of three raw materials A, B and C in the year 2009 and
2011 with their corresponding weightages. Calculate the composite index in
year 2011 based on 2009.

Raw materials A BC
Price in 2009 (RM) 2.50 4.80 5.00
Price in 2011 (RM) 3.00 6.00 6.00
Weightage
5 23

121