Question

The median for the following distribution of 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

$$\begin{array}{ccc}\text{Class Interval}& \text{Frequency}& \text{Cumulative Frequency}\\ 60-70& 2& 2\\ 70-80& 3& 5\\ 80-90& 5& 10\\ 90-100& 16& 26\\ 100-110& 14& 40\\ 110-120& 13& 53\\ 120-130& 7& 60\end{array}$$ $\frac{n}{2}=30$.
So, the median class is the one whose cumulative frequency is closest to and greater than 30.
$\therefore$ The median class is 100-110

$Median=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
Where $l$ is lower class limit of median class.
$n$ is total number of observations.
$cf$ is the cumulative frequency of the class preceding the median class.
$f$ is the frequency of the median class and h is the class size.

$⟹Median=100+\frac{30-26}{14}\times 10$

$\therefore Median=102.86$