Find the mode of the following frequency distribution of marks obtained by $50$ students.
Marks obtained $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
No. of students $5$ $12$ $20$ $10$ $3$

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Solution

$\Rightarrow$ Here, maximum frequency is $20$ .
$∴$ Modal class $= 20 - 30$
So, $l = 20, f_{0} = 12, f_{1} = 20, f_{2} = 10$ and $h = 10$
$\Rightarrow$ $M o d e = l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$
$= 20 + \frac{20 - 12}{2 \times 20 - 12 - 10} \times 10$
$= 20 + \frac{8}{18} \times 10$
$= 20 + 4.44$
$= 24.44$

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