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	11	10	7	4	4

Answer 1

To find the class mark (\(x_i\)) for each interval, the following relation is used.  

Class mark  \((x_i)\) = \(\frac {\text{Upper \,limit + Lower \,limit}}{2}\)

class size (h) of the data = 10

Taking 70 as assumed mean (a), \(d_i\), \(u_i\), and \(f_iu_i\) can be calculated as follows.   

Literacy rate (in %)	Number of cities \(\bf{f_i}\)	\(\bf{x_i}\)	\(\bf{d_i = x_i -70}\)	\(\bf{u_i = \frac{d_i}{10}}\)	\(\bf{f_iu_i}\)
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
Total	35				-2

From the table, We obtain

\(\sum f_i = 35\)
\(\sum f_iu_i = -2\)

Mean, \(\overset{-}{x} = a + (\frac{\sum f_iu_i}{\sum f_i}) \times h\) 

x = \(70 + (-\frac{2}{35})\times (10)\) 

x = 70 - \(\frac{20}{35}\) 

x = 70 - \(\frac{4}5\)

x = 70 - 0.57
x = 69.43

Therefore, mean literacy rate is 69.43%.