Question

Compute the mean marks obtained by the students from the following data:

Marks	0−10	10−20	20−30	30−40	40−50
No. of Students	4	6	10	20	10

Answer 1

Class Interval	Mid Values $\mathit{m}\mathbf{=}\frac{{\mathit{l}}_{\mathbf{1}}\mathbf{+}{\mathit{l}}_{\mathbf{2}}}{\mathbf{2}}$	Students (f)	fm
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50	5 15 25 35 45	4 6 10 20 10	20 90 250 700 450
		Σf= 50	Σfm= 1510

Calculating mean marks using direct method:

$$\begin{gathered} \overline{X}=\frac{\Sigma fm}{\mathrm{\Sigma }f} \\ \mathrm{Here}, \\ m=\frac{\mathrm{lower}\mathrm{limit}\left(l_1\right)+\mathrm{upper}\mathrm{limit}\left(l_2\right)}{2} \\ \overline{X}=\frac{1510}{50} \\ \Rightarrow \overline{X}=30.2\mathrm{marks} \end{gathered}$$

Hence, mean marks obtained by the students are 30.2