Question

There is a class of $50$ students writing an exam for $100$ marks. The middle value of all scores is found out to be $35.5$ marks. It was also observed that mark $60$ had the highest frequency of occurrence. Now the teacher wants to find the mean value of whole lot of students. Find the mean value.

• A. $22.5$
• B. $23.25$
• C. $25.46$
• D. $23.5$

Answer 1

Answer: (B)

$23.25$

Given data : Median $=35.5$
Mode $=60$
We know $[3\times \text{median}=\text{mode}+2\times \text{mean}]$
Therefore, $3\times 35.5=60+2\times \text{mean}$
$\Rightarrow 106.5=60+2\times \text{mean}$
$\Rightarrow 106.5-60=2\times \text{mean}$
$\Rightarrow 46.5=2\times \text{mean}$
Mean $=\frac{46.5}{2}$
Mean $=23.25$