Question

The table below shows students in a class sorted according to their marks in a Maths exam :

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ 0-10& 4\\ 10-20& 12\\ 20-30& 10\\ 30-40& 8\\ 40-50& 6\end{array}$

Calculate the Median mark

• A. 23
• B. 22
• C. 24
• D. 25.5

Answer 1

The correct option is C

24

$\begin{array}{ccc}\text{Marks}& \text{No. of students}& \text{Cumulative frequency}\\ \text{Below}10& 4& 4\\ \text{Below}20& 12& 16\\ \text{Below}30& 10& 26\\ \text{Below}40& 8& 34\\ \text{Below}50& 6& 40\end{array}$

Here we see n = 40

So , we need the marks of the 20th and 21st student to find the Median

The marks of these 2 students lie in the range of 20-30

Now we have to divide this range into 10 equal parts.

We take it as 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29

The marks of the 20th student is given by $\frac{23+24}{2}$ = 23.5

The marks of the 21st student is given by $\frac{24+25}{2}$ = 24.5

$\therefore$ Median is given by $\frac{23.5+24.5}{2}$ = $\frac{48}{2}$ = 24