Question

If the median of the following data is 50, then find the value of $p$.
$$\begin{array}{cc}\text{Class}& \text{Frequency}\\ \text{0 - 20}& 10\\ \text{20 - 40}& 7\\ \text{40 - 60}& 16\\ \text{60 - 80}& p\\ \text{80 - 100}& 8\end{array}$$

• A. 6
• B. 9
• C. 8
• D. 7

Answer 1

The correct option is B 9

The cumulatice frequency distribution table is given below:
$\begin{array}{ccc}\text{Class}& \text{Frequency}& CumulativeFrequency\\ \text{0 - 20}& \text{10}& \text{10}\\ \text{20 - 40}& \text{7}& \text{17}\\ \text{40 - 60}& \text{16}& \text{33}\\ \text{60 - 80}& \text{p}& \text{33+p}\\ \text{80 -100}& \text{8}& \text{41+p}\end{array}$

Since median is 50, median class is 40-60.

Using;
$Median=l+\left[\frac{\frac{n}{2}-cf}{f}\right]\times h$,
$Here,n=41+p,$
$⟹\frac{n}{2}=\frac{(41+p)}{2}$
$Now,50=40+[\frac{\frac{(41+p)}{2}-17}{16}\times 20]$
$⟹10=[\frac{\frac{(41+p-34)}{2}}{16}\times 20]$
$⟹10=[\frac{(7+p)}{16\times 2}\times 20]$
Simplifying, we get $\frac{(7+p)}{16}=1$
$\Rightarrow 7+p=16$
$\Rightarrow p=9$
$\therefore$ the value of $p$ is 9.