Question

Find out the mean of the following distribution:

Items	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	5	7	13	21	16	8	3

Answer 1

Items	Mid value $\left(\mathit{m}\mathit{=}\frac{{\mathit{l}}_{\mathit{1}}\mathit{+}{\mathit{l}}_{\mathit{2}}}{\mathit{2}}\right)$	Frequency (f)	Multiplication of mid value and frequency (fm)
0 − 5	$\frac{0+5}{2}=2.5$	2	5
5 − 10	$\frac{5+10}{2}=7.5$	5	37.5
10 − 15	$\frac{10+15}{2}=12.5$	7	87.5
15 − 20	$\frac{15+20}{2}=17.5$	13	227.5
20 − 25	$\frac{20+25}{2}=22.5$	21	472.5
25 − 30	$\frac{25+30}{2}=27.5$	16	440
30 − 35	$\frac{30+35}{3}=32.5$	8	260
35 − 40	$\frac{35+40}{2}=37.5$	3	112.5
		Σf = 75	Σfm = 1642.5

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathit{\Sigma }\mathit{f}\mathit{m}}{\mathit{\Sigma }\mathit{f}} \\ \mathrm{or},\overline{X}=\frac{1642.5}{75} \\ \Rightarrow \overline{X}=21.9 \end{gathered}$$

Hence, the mean of the above distribution is 21.9