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%.