Question

$$\begin{array}{cccccc}\text{Marks}& \text{Below 10}& \text{Below 20}& \text{Below 30}& \text{Below 40}& \text{Below 50}\\ \text{No. of students}& 5& 10& 23& 31& 40\end{array}$$
The median for the data given above is ____.

• A. 26.79
• B. 27.69
• C. 29.67
• D. 26.69

Answer 1

The correct option is B 27.69

The given table can be re-written as follows:
$$\begin{array}{cccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 5& 5& 13& 8& 9\\ \text{Cumulative Frequency}& 5& 10& 23& 31& 40\end{array}$$
In the above distribution the total number of observations is 40. Hence, n = 40.

$\frac{n}{2}=20$.

The cumulative frequency that is greater than 20 but closest to 20 is 23. The class corresponding to this frequency is 20-30. This is the median class.

Using Median = $l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
Where $l$ is lower class limit of median class.
$n$ is the 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.

$⟹Median=20+\frac{20-10}{13}\times 10$
$⟹Median=20+7.69$
$\therefore Median=27.69$