Question

​The following table shows the marks scored by 80 students in an examination:

Marks	Less than 5	Less than 10	Less than 15	Less than 20	Less than 25	Less than 30	Less than 35	Less than 40
Number of students	3	10	25	49	65	73	78	80

Calculate the mean marks correct to 2 decimal places.

Answer 1

Let us choose a = 17.5, h = 5, then d_i = x_i − 17.5 and u_{i =} $\frac{x_i-17.5}{5}$.

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 = $\frac{{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{17}\mathbf{.}\mathbf{5}}{\mathbf{5}}$	fiui
0−5	3	3	2.5	−15	−3	−9
5−10	10	7	7.5	−10	−2	−14
10−15	25	15	12.5	−5	−1	−15
15−20	49	24	17.5	0	0	0
20−25	65	16	22.5	5	1	16
25−30	73	8	27.5	10	2	16
30−35	78	5	32.5	15	3	15
35−40	80	2	37.5	20	4	8
Total		∑ fi = 80				∑ fiui = 17

The mean of given data is given by

$$\begin{gathered} \overline{x}=a+\left(\frac{{\displaystyle \sum _i}{f}_i{u}_i}{{\displaystyle \sum _i}{f}_i}\right)\times h \\ =17.5+\left(\frac{17}{80}\right)\times 5 \\ =17.5+1.06 \\ =18.56 \end{gathered}$$​

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