Question

Find the mean marks from the following data(nearest integer)

Marks	No. of Students
Below 10	5
Below 20	9
Below 30	17
Below 40	29
Below 50	45
Below 60	60
Below 70	70
Below 80	78
Below 90	83
Below 100	85

Answer 1

Changing less than type frequency distribution in general frequency distribution

Marks	$x_i$	$f_i$	$A=45,h=10$ $u_i=\frac{x-A}{h}$	$f_i{u}_i$
0 - 10	5	5	-4	-20
10 - 12	15	4	-3	-12
20 - 30	25	8	-2	-16
30 - 40	35	12	-1	-12
40 - 50	45	16	0	0
50 - 60	55	15	+1	15
60 - 70	65	10	+2	20
70 - 80	75	8	+3	24
80 - 90	85	5	+4	20
90 - 100	95	2	+5	10
		$\sum f_i=85$		$\sum f_i{u}_i=29$

According to step deviation formula for mean
$\overline{x}=A+(\frac{\sum f_i{u}_i}{\sum f_i}\times h)\Rightarrow \overline{x}=45+(\frac{29}{85}\times 10)\Rightarrow \overline{x}=45+3.41$
$\overline{x}=48.41$ So the mean marks is 48.41