Question

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

• 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.
$\frac{N}{2}=\frac{(41+p)}{2}$
$Median=40+[\frac{\frac{(41+p)}{2}-17}{16}\times 20]=50$
$[\frac{\frac{(41+p)}{2}-17}{16}\times 20]=10\Rightarrow \frac{(41+p)}{2}=25$

p = 9