Find the mode of the given data:

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$20$	$24$	$40$	$36$	$20$

Find the mode of the data using mode formula

We are given a continuous set of data.

For the data, class interval with highest frequency is called as modal class $20-30$ which have a frequency of $40$.

We know that, $\mathrm{mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)h$, where

$l=$lower limit of modal class

$f_1=$frequency of the modal class

$f_0=$frequency of the class preceding modal class

$f_2=$frequency of the class succeeding modal class

$h=$size of the class interval

So, the mode for modal class $20-30$ will be

$$\begin{gathered} \Rightarrow mode=20+\left(\frac{40-24}{(2\times 40)-24-36}\right)\times (30-20) \\ \Rightarrow mode=20+\left(\frac{16}{80-60}\right)\times 10 \\ \Rightarrow mode=20+\frac{16\times 10}{20} \\ \Rightarrow mode=20+8 \\ \Rightarrow mode=28 \end{gathered}$$

Hence, the mode of the data is $28$.