Question

Find the average age from the following data:

Age (in Years)	Less than 10	10−20	20−30	30−40	More than 40
No. of Persons	5	8	12	6	4

Answer 1

It must be noted that the given distribution is an open ended distribution, that is, the first and the last class interval are not explicitly defined. As mean is based on all the items in the series, so for such distributions mean cannot be calculated accurately. ​

However, going by the symmetry of the distribution we assume the first and the last class interval to be (0- 10) and (40 - 50), respectively

Age	Class Interval	Mid-Values (m)	Persons (f)	fm
Less than 10 10 − 20 20 − 30 30 − 40 more than 40	0 − 10 10 − 20 20 − 30 30 − 40 40 − 50	5 15 25 35 45	5 8 12 6 4	25 120 300 210 180
			$\mathit{\Sigma }\mathit{f}$=35	$\mathit{\Sigma }\mathit{f}\mathit{m}$=835

Computing average age:

$$\begin{gathered} \overline{\mathit{X}}=\frac{\Sigma fm}{\Sigma f} \\ or,\overline{X}=\frac{835}{35} \\ \Rightarrow \overline{X}=23.85\mathrm{years} \end{gathered}$$

Hence, average age is 23.85 years.