Find out the index numbers

Index Number || Average of Base Period

Question 
The following table gives the production of cotton cloth (in million yards) in Pakistan from 1954 to 1963.

Year	1954	1955	1956	1957	1958	1959	1960	1961	1962	1963
Production	282	389	438	470	511	555	564	630	662	681

Find out the index numbers by taking the:

1. 1954 as the base year
2. Average of 1958,59,60 as the base period.

Solution:

1. 1954 as the base year

Year Production		Price Relatives
		1954 as base year
1954	282	(282/282)*100=100
1955	389	(389/282)*100=137.94
1956	438	(438/282)*100=155.32
1957	470	(470/282)*100=166.67
1958	511	(511/282)*100=181.21
1959	555	(555/282)*100=196.81
1960	564	(564/282)*100=200
1961	630	(630/282)*100=223.40
1962	662	(662/282)*100=234.75
1963	681	(681/282)*100=241.49

ii.       Average of 1958,59,60 as the base period.

Average of 1958,59,60 =  `\frac{511 + 555 + 564}{3}` = `\frac{1630}{3}` = 543.33

Year Production		Price Relatives
		1954 as base year
1954	282	(282/543.33)*100=51.90
1955	389	(389/543.33)*100=71.59
1956	438	(438/543.33)*100=80.61
1957	470	(470/543.33)*100=86.50
1958	511	(511/543.33)*100=94.04
1959	555	(555/543.33)*100=102.15
1960	564	(564/543.33)*100=103.80
1961	630	(630/543.33)*100=115.95
1962	662	(662/543.33)*100=121.84
1963	681	(681/543.33)*100=125.34