Question

The table below gives the time (in seconds) 30 students take to solve a question.
$$\begin{array}{cc}Time& Number\\ & ofstudents\\ 20-60& 6\\ 60-100& 4\\ 100-140& 10\\ 140-180& 4\\ 180-220& 6\end{array}$$

• A. 100
• B. 120
• C. 110
• D. 130

Answer 1

The correct option is B 120

$\begin{array}{cc}Time& Cumulative\\ & frequency\\ 20-60& 6\\ 60-100& 10\\ 100-140& 20\\ 140-180& 24\\ 180-220& 30\end{array}$

Here, N = 30.
$\Rightarrow \frac{N}{2}=15$
$\therefore$ Median class is 100-140.

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:

$Median=100+\frac{\frac{30}{2}-10}{10}\times 40=100+20=120$