Question

The following table shows the age of workers in a factory. Find out the average age of workers.

Age (in Years)	20−29	30−39	40−49	50−59	60−69
Workers	10	8	6	4	2

Answer 1

Calculation of mean in an inclusive series:

Class Interval (Age)	Mid-Values (m)	Workers (f)	fm
20 − 29 30 − 39 40 − 49 50 − 59 60 − 69	24.5 34.5 44.5 54.5 64.5	10 8 6 4 2	245 276 267 218 129
		$\mathit{\Sigma }\mathit{f}$=30	$\mathit{\Sigma }\mathit{f}\mathit{m}$=1135

Computing the average age of workers:

$$\begin{gathered} \overline{\mathit{X}}=\frac{\Sigma fm}{\Sigma f} \\ or,\overline{X}=\frac{1135}{30} \\ \Rightarrow \overline{\mathit{X}}=37.83y\mathrm{ears} \end{gathered}$$

Hence, average age of workers is 37.83 years