Question

The following table shows the marks scored by 80 students in an examination:
$\begin{array}{ccccccccc}\text{Marks}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}& \text{Less}\\ & \text{than 5}& \text{than 10}& \text{than 15}& \text{than 20}& \text{than 25}& \text{than 30}& \text{than 35}& \text{than 40}\\ \text{Number of}& & & & & & & & \\ \text{students}& 3& 10& 25& 49& 65& 73& 78& 80\end{array}$
Calculate the mean marks correct to 2 decimal places.

Answer 1

Let us choose a = 17.5, h = 5,
then di = xi - 17.5
and ui = (xi−17.5)/5

Using Step-deviation method, the given data is shown as follows:

Marks	Number of students (cf)	Frequency (fi)	Class mark (xi)	di = xi- 17.5	ui = (xi−17.5)/5	fiui
Less than 5	3	3	2.5	-15	-3	-9
less than 10	10	7	7.5	-10	-2	-14
Less than 15	25	15	12.5	-5	-1	-15
Less than 20	49	24	17.5	0	0	0
less than 25	65	16	22.5	5	1	16
Less than 30	73	8	27.5	10	2	16
Less than 35	78	5	32.5	15	3	15
Less than 40	80	2	37.5	20	4	8
Total	∑fi=80					∑(fi×ui)=17

The mean of given data is given by

$\overline{x}$=a+(∑fiui/∑fi)×h

= 17.5 + 17/80 x 5

= 17.5 + 1.06

= 18.56

Thus, the mean mark correct to 2 decimal places is 18.56.