Question

Compute the mean of the following frequency distribution:

Class	0 − 20	20 − 40	40 − 60	60 − 80	80 − 100	100 – 120	120 – 140
Frequency	6	8	10	12	6	5	3

Answer 1

Here, h = 20

Let the assumed mean, A be 70.

Class	Mid-Values(xi)	Frequency (fi)	${\mathit{d}}_i\mathbf{=}{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{70}$	${\mathit{u}}_i\mathbf{=}\frac{{\mathit{x}}_i\mathbf{-}\mathbf{70}}{\mathbf{20}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
0−20	10	6	−60	−3	−18
20−40	30	8	−40	−2	−16
40−60	50	10	−20	−1	−10
60−80	70	12	0	0	0
80−100	90	6	20	1	6
100−120	110	5	40	2	10
120−140	130	3	60	3	9
		$\underset{}{\sum f_i=50}$			$\underset{}{\sum f_i{u}_i=-19}$

We know

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

∴ Mean of the given frequency distribution

$$\begin{gathered} =70+20\times \left(\frac{-19}{50}\right) \\ =70-7.6 \\ =62.4 \end{gathered}$$

Thus, the mean of the given frequency distribution is 62.4.