Question

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy rate (in %):	45 - 55	55 - 65	65 - 75	75 -85	85 - 95
Number of cities:	3	10	11	8	3

Answer 1

We may calculate class marks (x_i) for each interval by using the relation

x_i \(=\frac{Upper\,class\,limit+lower\,class\,limit}{2}\)

Class size (h) for this data = 10

Now taking 70 as assumed mean (A) we can calculate as follows:

Literacy rate (in %)	Number of cities (fi)	xi	di = xi - 70	ui = \(\frac{di}{10}\)	fiui
45 - 55	3	50	-20	-2	-6
55 - 65	10	60	-10	-1	-10
65 - 75	11	70	0	0	0
75 - 85	8	80	10	1	8
85 - 95	3	90	20	2	6
	N = 35				\(\sum\)fiui = -2

Mean (x̅) = A + \(\frac{\sum f_iu_i}{N}\times h\)

\(=70+\frac{-2}{35}\times10\)

\(=70-0.57\)

= \(69.43\)

So, 

mean literacy rate is 69.437