Question

Calculate arithemtic eman from the foolowing data:

Marks	No. Students
More than 0	150
More than 10	140
More than 20	100
More than 30	80
More than 40	80
More than 50	70
More than 60	30
More than 70	14

Answer 1

Converting more than cumulative frequency distribution into a simple frequency distribution

Marks	No. of students (c.f)
More than 0 More than 10 More than 20 More than 30 More than 40 More than 50 More than 60 More than 70	150 140 100 80 80 70 30 14

Class Interval	Mid-Values (m)	No. of students (f)	fm
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80	5 15 25 35 45 55 65 75	150-140=10 140-100=40 100-80=20 80-80=0 80-70=10 70-30=40 30-14=16 14-0=14	50 600 500 0 450 2200 1040 1050
		$\mathit{\Sigma }\mathit{f}$=150	$\mathit{\Sigma }\mathit{f}\mathit{m}$=5890

Calculating the mean marks by using direct method:

$$\begin{gathered} \overline{X}=\frac{\Sigma fm}{\Sigma f} \\ or,\overline{X}=\frac{5890}{150} \\ \Rightarrow \overline{X}=39.27marks \end{gathered}$$

Hence, the mean marks of the above series is 39.27