Question

Find the mean and variance for the following frequency distribution.

$\begin{array}{cccccccc}\text{Class}& 0-30& 30-60& 60-90& 90-120& 120-150& 150-180& 180-210\\ \text{Frequencies}& 2& 3& 5& 10& 3& 5& 2\end{array}$

Answer 1

$\begin{array}{cccccc}& \text{Mid values}& & & & \\ \text{Classes}& x_i& f_i& u=\frac{x-105}{30}& fu& f{u}^2\\ 0-30& 15& 2& -3& -6& 18\\ 30-60& 45& 3& -2& -6& 12\\ 60-90& 75& 5& -1& -5& 5\\ 90-120& 105& 10& 0& 0& 0\\ 120-150& 135& 3& 1& 3& 3\\ 150-180& 165& 5& 2& 10& 20\\ 180-210& 195& 2& 3& 6& 18\\ & & 30& & 2& 76\end{array}$

Mean $\left(\overline{x}\right)=A+\frac{\sum fu}{N}\times h=105+\frac{2}{30}\times 30=107$

Variance $\left({\sigma }^2\right)=\frac{h^2}{N^2}[N\sum f{u}^2-(\sum fu{)}^2]$