Question

Calculate the missing frequency from following distribution,it being given that the median of the distribution is 24.

$$\begin{array}{cccccc}Age\left(inyears\right)& 0-10& 10-20& 20-30& 30-40& 40-50\\ Numberof& & & & & \\ Persons& 5& 25& ?& 18& 7\end{array}$$

Answer 1

$\begin{array}{cccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 5& 25& ?& 18& 7\\ \text{cf}& 5& 30& 30+?& 48+?& 55+?\end{array}$
Since, the median class is given 24.
Therefore, median class = 20- 30
l =20 , h =10, cf = 30, $\frac{n}{2}$ = $\frac{55+x}{2}$
Median = l + $\frac{\frac{n}{2}-cf}{f}$ $\times$ h
24 = 20 + $\frac{\frac{55+x}{2}-30}{x}$ $\times$ 10
24-20 = $\frac{\frac{55+x}{2}-30}{x}$ $\times$ 10
4 = $\frac{\frac{55+x}{2}-30}{x}$ $\times$ 10
0.4 = $\frac{\frac{55+x}{2}-30}{x}$
0.4x = $\frac{55+x-60}{2}$
0.8x = x-5
5 = 0.2 x
x = 25