Question

The table given below shows the age distribution of 1000 persons who visited a marketing centre on a Sunday.

Age (in years)	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50	50 – 60	60 – 70
Number of persons	105	222	220	138	102	113	100

Find the mean age of the persons visiting the marketing centre on that day.

Answer 1

Here, h = 10

Let the assumed mean, A be 35.

Age (in years)	Mid-Values(xi)	Number of persons (fi)	${\mathit{d}}_i\mathbf{=}{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{35}$	${\mathit{u}}_i\mathbf{=}\frac{{\mathit{x}}_i\mathbf{-}\mathbf{35}}{\mathbf{10}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
0−10	5	105	−30	−3	−315
10−20	15	222	−20	−2	−444
20−30	25	220	−10	−1	−220
30−40	35	138	0	0	0
40−50	45	102	10	1	102
50−60	55	113	20	2	226
60−70	65	100	30	3	300
		$\underset{}{\sum f_i=1000}$			$\underset{}{\sum f_i{u}_i=-351}$

We know

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

∴ Mean age of the persons visiting the marketing centre on that day

$$\begin{gathered} =35+10\times \left(\frac{-351}{1000}\right) \\ =35-3.51 \\ =31.49 \end{gathered}$$

Thus, the mean age of the persons visiting the marketing centre on that day 31.49 years.