Question

The following is the cumulative frequency distribution ( of less than type ) of 1000 persons each of age 20 years and above . Determine the mean age .

Age below (in years) : 30 40 50 60 70 80

Number of persons: 100 220 350 750 950 1000

Answer 1

Let the assumed mean A = 55 and h = 10.

Marks	Mid-Value	Frequency	${\mathit{u}}_{\mathbf{i}}\mathbf{=}\frac{{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{55}}{\mathbf{10}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
20–30	25	100	−3	−300
30–40	35	120	−2	−240
40–50	45	130	−1	−130
50–60	55	400	0	0
60–70	65	200	1	200
70–80	75	50	2	100
		N = 1000		$\sum _{}{f}_i{u}_i=-370$

We know that mean,
Now, we have $N=\sum _{}{f}_i=1000,h=10,A=55,\sum _{}{f}_i{u}_i=-370$
$$\begin{gathered} \overline{X}=55+10\left[\frac{1}{1000}\times \left(-370\right)\right] \\ =55-3.7 \\ =51.3\mathrm{years} \end{gathered}$$