Question

Compute the mode of the following distribution:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$2$	$5$	$10$	$5$	$4$	$3$

Answer 1

Step 1: Finding different values of mode formula

Given table:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$2$	$5$	$10$	$5$	$4$	$3$

From the above table, we can see that the class $20-30$ has a maximum frequency, so the modal class is $20-30$.

For determining the mode we will use the formula:

$\mathrm{Mode}=l+\left(\frac{{\mathrm{f}}_1-{\mathrm{f}}_0}{2{\mathrm{f}}_1-{\mathrm{f}}_0-{\mathrm{f}}_2}\right)\times h$

Where, $l$ = Lower limit of modal class $(20-30)=20$

$h$ = Size of the class-interval $=10$

$f_1$ = Frequency of the modal class $=10$

$f_0$ = Frequency of the class preceding the modal class $=5$

$f_2$ = Frequency of the class succeeding the modal class $=5$

Step 2: Finding the mode

Substituting the values in the mode formula:

$$\begin{gathered} Mode=20+\left(\frac{10-5}{2\times 10-5-5}\right)\times 10 \\ =20+\left(\frac{5}{10}\right)\times 10 \\ =20+5 \end{gathered}$$

$\therefore Mode=25$

Hence, the mode of distribution is $25$.