Chapter 11 index number
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This document discusses index numbers and how to calculate price indexes, composite indexes, and uses examples to demonstrate these calculations. It provides information on how price indexes track price changes over time for individual items and how composite indexes track changes in the overall cost of multiple items using price indexes and weightings. Formulas and steps are given for calculating price indexes, composite indexes, and using them to find item prices or total costs in different years. Exercises provide additional practice calculating various index numbers.
Chapter 11 index number
- 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.