Question

Calculate the mode of the following data:

Class-interval	$15-25$	$25-35$	$35-45$	$45-55$	$55-65$	$65-75$	$75-85$
Frequency	$5$	$4$	$7$	$12$	$8$	$1$	$4$

Answer 1

Step 1: Finding different values of mode formula

Given table:

Class-interval	$15-25$	$25-35$	$35-45$	$45-55$	$55-65$	$65-75$	$75-85$
Frequency	$5$	$4$	$7$	$12$	$8$	$1$	$4$

From the above table, we can see that the class $45-55$ has a maximum frequency, so the modal class is $45-55$.

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 $(45-55)=45$

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

$f_1$ = Frequency of the modal class $=12$

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

$f_2$ = Frequency of the class succeeding the modal class $=8$

Step 2: Finding the mode

Substituting the values in the mode formula:

$$\begin{gathered} Mode=45+\left(\frac{12-7}{2\times 12-7-8}\right)\times 10 \\ =45+\left(\frac{5}{9}\right)\times 10 \\ =45+5.56 \end{gathered}$$

$\therefore Mode=50.56$

Hence, the mode of the data is $50.56$.