Question

The table below gives the number of non-stop pushups that 40 college students claim they can easily do.
Find the median of this data set.
$$\begin{array}{cc}\text{Number}& \text{Number}\\ \text{of pushups}& \text{of students}\\ 35-41& 6\\ 41-47& 8\\ 47-53& 8\\ 53-59& 12\\ 59-65& 6\end{array}$$

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

The correct option is A 10

$\begin{array}{ccc}Class& Frequency& Cumulative\\ Interval& & Frequency\\ 35-41& 6& 6\\ 41-47& 8& 14\\ 47-53& 8& 22\\ 53-59& 12& 34\\ 59-65& 6& 40\end{array}$

Here, N = 40.
$\Rightarrow \frac{N}{2}=20$
$\therefore$ Median class is 47-53.

The formula for median of a grouped data is given by,

$M=L+\left[\frac{\frac{n}{2}-cf}{f}\right]\times h$
where,
M = median of the grouped data
L = Lower limit of median class
n = Sum of frequencies
cf = Cumulative frequency of the class preceding the median class
f = frequency of the median class
and, h = class size

Substituting the given values, we get:

$Median=47+\frac{\frac{40}{2}-14}{8}\times 6=47+\frac{9}{2}=51.5$