Question

The median class for the following data is
$$\begin{array}{cccccc}\text{Marks}& Below10& Below20& Below30& Below40& Below50\\ \text{No. of students}& 5& 10& 23& 31& 40\end{array}$$

• A. 10 - 20
• B. 20 - 30
• C. 30 - 40
• D. 40 - 50

Answer 1

The correct option is B

20 - 30

The given table can be written as:
$$\begin{array}{cccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{No. of students}& 5& 5& 13& 8& 9\\ \text{Cumulative Frequency}& 5& 10& 23& 31& 40\end{array}$$
No. of students can be calculated as follows:
5
10 - 5 = 5
23 - 10 = 13
31 - 23 = 8
40 - 31 = 9

$\therefore \frac{n}{2}=\frac{40}{2}=20$

Since there are a total of 40 observations, the median class is the one whose cumulative frequency is closest to and greater than 20.

Here the cumulative frequency for the class interval '10 - 20' is 23 which is greater than 20.

The class interval 20 - 30 is the required answer.