Question

Find the mean age from the following frequency distribution:

Age (in years)	25-29	30-34	35-39	40-44	45-49	50-54	55-59
No. of person	4	14	22	16	6	5	3

Answer 1

Converting the series into exclusive form, we get:

Class	Frequency$\left(f_i\right)$	Mid values$\left(x_i\right)$	$$\begin{gathered} u_i=\frac{(x_i-A)}{h} \\ \text{=}\frac{(x_i-42)}{5} \end{gathered}$$	$(f_i\times u_i)$
24.5-29.5	4	27	−3	−12
29.5-34.5	14	32	−2	−28
34.5-39.5	22	37	−1	−22
39.5-44.5	16	42 = A	0	0
44.5-49.5	6	47	1	6
49.5-54.5	5	52	2	10
54.5-59.5	3	57	3	9
	$\sum f_i=70$			$\sum (f_i\times u_i)=-37$

$$\begin{gathered} \text{Now,}A=42,h=5,\sum f_i=70\mathrm{and}\sum (f_{{}_i}\times u_i)=-37 \\ \therefore \text{Mean,}\overline{x}=A+\{h\times \frac{{\displaystyle \sum (f_{{}_i}\times u_i)}}{{\displaystyle \sum f_i}}\} \\ \text{=42+}\{5\times \frac{(-37)}{70}\} \\ \text{=42-2}\text{.64} \\ \text{=39}\text{.36} \\ \therefore \overline{x}=39.36 \\ \therefore \text{Mean age=39}\text{.36 years} \end{gathered}$$