1. Additional Mathematics Module Form 4
Chapter 11- Index Number SMK Agama Arau, Perlis
Page | 145
CHAPTER 11- INDEX NUMBER
11.1 INDEX NUMBER
1. An index number is a statistical measure to show the changes of any variable such as prices,
production and many others with respect to time.
2. The formula of to calculate index number is
where 0Q = Quantity at base time
1Q = Quantity at specific time
11.1.1 Price Index
1. Price index is an example of index number which is widely used.
2. It tells us how the price changes over a fixed period of time.
3. Price index of a certain item, 100
0
1
×=
Q
Q
I where:
(a) 0Q = Price of the item at the base time or year
(b) 1Q = Price of the item at specific time
Example 1:
In a year, a copy of newspaper was sold at RM1.20. However, in a year, 2008, a consumer has to pay
RM1.50 for the same copy of newspaper. Calculate the price index of the newspaper for the year 2008 if
the year 2007 is taken as the base year.
Solution:
0Q (Price of the item at the base year that is 2007) = RM1.20
1Q (Price of the item at specific time that is year 2008) = RM1.50
100
07
08
07,08 ×=
Q
Q
I
125
100
20.1
50.1
=
×=
RM
RM
100
0
1
×=
Q
Q
I

2. Additional Mathematics Module Form 4
Chapter 11- Index Number SMK Agama Arau, Perlis
Page | 146
Example 2:
The price index of a product in the year 1998 is 120 based on the year 1994 and 130 based on the year
1991. If the price of the product in 1994 is RM 650, calculate the price in the year 1991.
Solution:
From the information above, given that 12094,98 =I , 13091,98 =I and 65094 RMQ =
100
94
98
94,98 ×=
Q
Q
I
Substitute 12094,98 =I and 65094 RMQ = into the formula above,
750
100
650
120
98
98
RMQ
Q
=
×=
100
91
98
91,98 ×=
Q
Q
I
Substitute 13091,98 =I and 75098 RMQ = into the formula above,
600
100
750
130
91
91
RMQ
Q
RM
=
×=
The price of the product in the year 1991 is RM600.
100
94
91
94,91 ×=
Q
Q
I
30769231.92
100
650
600
=
×=
RM
RM
100
91
94
91,94 ×=
Q
Q
I
3333333.108
100
600
650
=
×=
RM
RM

3. Additional Mathematics Module Form 4
Chapter 11- Index Number SMK Agama Arau, Perlis
Page | 147
100
94,91
94,94
91,94 ×=
I
I
I
3333333.108
100
30769231.92
100
=
×=
100
91,9494,98
91,98
II
I
×
=
130
100
3333333.108120
=
×
=
100
94,91
94,98
91,98 ×=
I
I
I
130
100
30769231.92
120
=
×=
The other formula to find price index is
Besides 91,94I can be calculated by
100
91
94
91,94 ×=
Q
Q
I
While
Besides 91,98I can be calculated by
100
91
98
91,98 ×=
Q
Q
I
These three formulae can be used to calculate price index in certain situations.
100
94,91
94,94
91,94 ×=
I
I
I
100
91,9494,98
91,98
II
I ×
=
100
94,91
94,98
91,98 ×=
I
I
I

4. Additional Mathematics Module Form 4
Chapter 11- Index Number SMK Agama Arau, Perlis
Page | 148
EXERCISE 11.1
1. A factory produces 10000 cans of drink in the year 2000 and 12000 cans in the year 2001. Calculate
the index number for the production of cans of drink in the year 2001 based on the year 2000.
2. The total salary of Ammar Fauzan in the year 1999 is RM 14400 and in the year 2000 is RM20000.
Calculate the index number for his salary in the year 2000 based on the year 1999.
3. The index numbers for an item in the years 2001 and 2002, based on the year 1997, are 108 and 120
respectively. Calculate:
(a) the index number in the year 1997 based on the year 2002.
(b) the index number in the year 2002 based on the year 2001.
11.2 COMPOSTE INDEX NUMBER
1. The formula for composite index is
where I is price index and w is weightage.
2. For example to find the composite index number is the monthly of a family.
(a) In determining the composite index number of the monthly expenditure, we need to consider
the price indices and weightages f all the items.
(b) Items that we spend more will definitely play more significant role and hence, is assigned with a
larger weightage.
Example:
Things Price Index Weightage
Shirt 120 m
Trousers 105 8
Bag 140 4
Shoes 150 6
Table 1
The table shows the price indices and the weightage of four things in 1997 based on the year 1992.
Given that the composite index of 1992 is 127. Calculate:
(a) The value of m
(b) The price of a pair of shoes in 1997 if its price in 1992 is RM60.
Solution:
(a) We know that the formula for composite index is
∑
∑=
−
w
Iw
I
∑
∑=
−
w
Iw
I Weightage, w represents the
relative importance of different
items
Info…

5. Additional Mathematics Module Form 4
Chapter 11- Index Number SMK Agama Arau, Perlis
Page | 149
Use the information given.
648
)6(150)4(140)8(105)(120
+++
+++
=
−
m
m
I
18
900560840120
+
+++
=
−
m
m
I
Given that 12792,97 =
−
I ,
22861272300120
127
18
900560840120
+=+
=
+
+++
mm
m
m
2
147
=
=
m
m
(b)From the information in the table, given that 150)(92,97 =ShoesI , 13091,98 =I and 6092 RMQ = ,
100)(
92
97
92,97 ×=
Q
Q
ShoesI
Substitute 150)(92,97 =ShoesI , 13091,98 =I and 6092 RMQ = into the formula above,
90
100
60
150
97
97
RMQ
RM
Q
=
×=
The price of shoes in the year 1992 is RM90.
EXERCISE 11.2
1. Table 2 shows the index numbers for three items P, Q and R in the years 2005 and 2006 based on the
year 2002. The composite index in the years 2005 and 2006 based on the year 2002 are 115.3 and
123.4 respectively.
Item Year 2005 Year 2006 Weightage
P 115 124 3
Q 120 x 5
R 104 126 y
Table 2
Find the value of x and of y.
2. Table 3 shows the index numbers for 3 items for 3 items in the year 2005 based on the year 2000.
Item P Q R
Index Number 115 98 124
Weightage 8 x 12- x
Table 3
Given that the composite index is 117.8, calculate the value of x.

6. Additional Mathematics Module Form 4
Chapter 11- Index Number SMK Agama Arau, Perlis
Page | 150
CHAPTER REVIEW EXERCISE
1. Table 4 shows the prices and weightages of four types of items A,B ,C and D.
Item
Price(RM) Price(RM)
Price Index Weightage
Year 2003 Year 2005
A 7.00 8.40 w 100
B 13.50 x 130 80
C y 13.00 115 70
D 11.00 12.10 110 z
Table 4
(a) Calculate the value of w, x and y.
(b) The composite index of these items for the year 2005 based on the year 2003 is 120. Calculate the
value of z.
(c) The total cost of all these items is expected to increase by 20% from the year 2005 to the year 2007.
Find the expected composite index for the year 2007 based on the year 2003.
2. Table 5 shows the index numbers for 5 items in a town in the year 2005 based on the year 2003 and
their weightages.
Item Index Number Weightage
Food 128 23
Drink 115 5
Clothing 119 5
Rental 124 4
Electricity 110 3
Table 5
(a) Calculate the composite index in year 2005 based on the year 2003.
(b) If the rental in the year 2005 is RM400, what is the rental in the year 2003?
(c) If the total expenditure of a family in the year 2003 is RM320, find the total expenditure in the year
2005.