Question

A polling agency interviewed 200 persons. The age distribution of those persons was recorded as under:

Age (Years)	80−89	70−79	60−69	50−59	40−49	30−39	20−29	10−19
Frequency	2	2	6	20	56	40	42	32

Calculate mean age of the persons by Direct Method.

Answer 1

Age	Mid Value (m) $\left(\mathit{m}\mathbf{=}\frac{{\mathit{l}}_{\mathbf{1}}\mathbf{+}{\mathit{l}}_{\mathbf{2}}}{\mathbf{2}}\right)$	Frequency (f)	fm
10 − 19	$\frac{10+19}{2}=14.5$	32	464
20 − 29	$\frac{20+29}{2}=24.5$	42	1029
30 − 39	$\frac{30+39}{2}=34.5$	40	1380
40 − 49	$\frac{40+49}{2}=44.5$	56	2492
50 − 59	$\frac{50+59}{2}=54.5$	20	1090
60 − 69	$\frac{60+69}{2}=64.5$	6	387
70 − 79	$\frac{70+79}{2}=74.5$	2	149
80 − 89	$\frac{80+89}{2}=84.5$	2	169
		Σf = 200	Σfm = 7160

Calculating the mean by Direct method:

$$\begin{gathered} \overline{\mathit{X}}=\frac{\Sigma fm}{\Sigma f} \\ \mathrm{or},\overline{X}=\frac{7160}{200} \\ \Rightarrow \overline{X}=35.8 \end{gathered}$$

Hence,mean age of the persons is 35.8 years.