Question

Compute the mode of the following data:

Class-interval	$0-5$	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$
Frequency	$2$	$7$	$18$	$10$	$8$	$5$

Answer 1

Calculating the mode:

The given information is

Class-interval	$0-5$	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$
Frequency	$2$	$7$	$18$	$10$	$8$	$5$

The formula for mode is

$\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathbf{}\mathbf{=}\mathbf{}\mathit{l}\mathbf{+}\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\mathbf{\times }\mathit{h}$

Here the class $10-15$ has a maximum frequency, so the modal class is $10-15$.

So,

$l$ = Lower limit of $10-15$ is $10$

$h$ = Size of the class-interval $=5$

$f_1$ = Frequency of the modal class $=18$

$f_0$ = Frequency of the class preceding the modal class $=7$

$f_2$ = Frequency of the class succeeding the modal class $=10$

Therefore,

$$\begin{gathered} Mode=10+\left(\frac{18-7}{2\times 18-7-10}\right)\times 5 \\ \Rightarrow Mode=10+\left(\frac{11}{19}\right)\times 5 \\ \Rightarrow Mode=10+2.89 \\ \therefore Mode=12.89 \end{gathered}$$

Hence the mode of the given data is $12.89$.