Question

Find the mode of the following frequency distribution:
$\begin{array}{cccccc}\text{Marks}& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequency}& 12& 35& 45& 25& 13\end{array}$

Answer 1

As the class 30-40 has maximum frequency, so it is the modal class:

Using, $Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\ast h$

where

l = lower limit of the modal class,

h = size of the class interval (assuming all class sizes to be equal),

$f_1$ = frequency of the modal class,

$f_0$ = frequency of the class preceding the modal class,

$f_2$ = frequency of the class succeeding the modal class.

$Mode=30+\left(\frac{45-35}{2\ast 45-35-25}\right)\ast 10$

$\Rightarrow Mode=30+\left(\frac{10}{30}\right)\ast 10$

$\Rightarrow Mode=30+3.33$

$\Rightarrow Mode=33.33$