Question

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

• A. 6
• B. 7
• C. 8
• D. 9

Answer 1

The correct option is D

9

$\begin{array}{ccc}\text{Class}& \text{Frequency}& CumulativeFrequency\\ \text{0-20}& \text{10}& \text{10}\\ \text{20-40}& \text{7}& \text{17}\\ \text{40-60}& \text{16}& \text{33}\\ \text{60-80}& \text{p}& \text{33+p}\\ \text{80-100}& \text{8}& \text{41+p}\end{array}$

Since median is 50, median class is 40-60.
$\frac{n}{2}=\frac{(41+p)}{2}$
median = 40 + $[\frac{\frac{(41+p)}{2}-17}{16}\times 20]$ = 50
$[\frac{\frac{(41+p)}{2}-17}{16}\times 20]$ = 10
Simplifying, we get $\frac{(41+p)}{2}$ = 25
Or, p = 9