Question

Question 9
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

$\begin{array}{cccccc}\text{Literacy rate (in \%)}& 45-55& 55-65& 65-75& 75-85& 85-95\\ \text{Number of cities}& 3& 10& 11& 8& 3\end{array}$

Answer 1

We may find the class marks by using the relation:

$x_i=\frac{\text{Upper class limit + lower class limit}}{2}$

Class size $h$ for this data = 10

Now, taking 70 as assumed mean $a$, we may calculate $d_i,u_i,and{f}_i{u}_i$ as following:

$\begin{array}{cccccc}\text{Literacy rate (in \%)}& \text{Number of cities}{f}_i& x_i& d_i=x_i-70& d_i/h& f_i{u}_i\\ 45-55& 3& 50& -20& -2& -6\\ 55-65& 10& 60& -10& -1& -10\\ 65-75& 11& 70& 0& 0& 0\\ 75-85& 8& 80& 10& 1& 8\\ 85-95& 3& 90& 20& 2& 6\\ \text{Total}& 35& & & & -2\end{array}$

Now, we may observe that:

$\sum f_i=35\sum f_i{u}_i=-2\text{mean}\overline{x}=a+\left(\frac{\sum f_i{u}_i}{\sum u_i}\right)\times h=70+\left(\frac{-2}{35}\right)\times \left(10\right)=70-\frac{20}{35}$

= 70 - 0.57

= 69.43

So, mean literacy rate is $69.43\%$.