Question

The median for the data is :

$\begin{array}{cccccccc}\text{IQ}& 60-70& 70-80& 80-90& 90-100& 100-110& 110-120& 120-130\\ \text{No. of pupils}& 2& 3& 5& 16& 14& 13& 7\end{array}$

• A. 102.86
• B. 98.46
• C. 97.47
• D. 103.26

Answer 1

The correct option is A

102.86

n = 60

The median for grouped data is given by $\frac{n}{2}$ = $\frac{60}{2}$ = 30th Observation

$\begin{array}{ccc}\text{Class Interval}& \text{Frequency}& \text{Cumulative Frequency}\\ 60-70& 2& 2\\ 70-80& 3& 5\\ 80-90& 5& 10\\ 90-100& 16& 26\\ 100-110& 14& 40\\ 110-120& 13& 53\\ 120-130& 7& 60\end{array}$

As we can see from the table ,

The 30th observation lies in the range 100-110

There are 14 values in this range.

Taking the step jump method we get :

$\frac{Interval}{No.ofvalues}$ = $\frac{5}{7}$ = 0.7 approximately

If we start jumping from 100 we get :

100+0.7 , 100 + 1.4 , 100 + 2.1 , 100 + 2.8 , 100 + 3.5 and so on.... for this interval

The 30th Observation will lie between 100 + 2.8 and 100 + 3.5 (between 4th and 5th)

The 30th Observation = $\frac{102.8+103.5}{2}$ = 103.15

$\therefore$ The median is 103.15