Question

Find arithmetic mean from the following distribution:

Marks	0−4	4−8	8−12	12−16
Number of Students	4	8	2	1

Answer 1

Marks	Mid value (m) $\left(\mathit{m}\mathit{=}\frac{{\mathit{l}}_{\mathit{1}}\mathit{+}{\mathit{l}}_{\mathit{2}}}{\mathit{2}}\right)$	No. of student (f)	Multiplication of mid-value and frequency (fm)
0 − 4	$\frac{0+4}{2}=2$	4	8
4 − 8	$\frac{4+8}{2}=6$	8	48
8 − 12	$\frac{8+12}{2}=10$	2	20
12 − 16	$\frac{12+16}{2}=14$	1	14
		Σf = 15	Σfm = 90

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathit{\Sigma }\mathit{f}\mathit{m}}{\mathit{\Sigma }\mathit{f}} \\ \mathrm{or},\overline{X}=\frac{90}{15} \\ \Rightarrow \overline{X}=6 \end{gathered}$$

Hence, the mean marks of the above distribution is 6.