Question

Find the mean of the following data.

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$5$	$8$	$13$	$15$	$9$

Answer 1

Step 1: Completing the table

By finding the sum of frequencies and the sum of the product of frequency and mid-value, we have completed the table as,

Class-interval	Mid-value $x_i$	Frequency $f_i$	$f_i{x}_i$
$10-20$	$15$	$5$	$75$
$20-30$	$25$	$8$	$200$
$30-40$	$35$	$13$	$455$
$40-50$	$45$	$15$	$675$
$50-60$	$55$	$9$	$495$
		$\Sigma f_i=50$	$\Sigma f_i{x}_i=1900$

Step 2: Finding mean

The formula for mean is $\overline{x}=\frac{\Sigma f_i{x}_i}{\Sigma f_i}$.

where $\Sigma f_i$ is the total frequency and $x_i$ is the mid-value of class-intervals.

Substituting the values in the formula for mean,

$$\begin{gathered} \Rightarrow \overline{x}=\frac{1900}{50} \\ \therefore \overline{x}=38 \end{gathered}$$

Hence, the mean is obtained as $38$.