Question

Compute the mean of the following frequency distribution:

Class	10 − 30	30 − 50	50 − 70	70 − 90	90 − 110
Frequency	15	18	25	10	2

Answer 1

Here, h = 20

Let the assumed mean, A be 60.

Class	Mid-Values(xi)	Frequency (fi)	$d_i=x_i-60$	$u_i=\frac{x_i-60}{20}$	$f_i{u}_i$
10−30	20	15	−40	−2	−30
30−50	40	18	−20	−1	−18
50−70	60	25	0	0	0
70−90	80	10	20	1	10
90−110	100	2	40	2	4
		$\underset{}{\sum f_i=70}$			$\underset{}{\sum f_i{u}_i=-34}$

We know

Mean $=A+h\times \left(\frac{{\sum }^{}{f}_i{u}_i}{{\sum }^{}{f}_i}\right)$

∴ Mean of the given frequency distribution

$=60+20\times \left(\frac{-34}{70}\right)=60-9.71=50.29\left(\mathrm{Approx}\right)$

Thus, the mean of the given frequency distribution is approximately 50.29.