Question

The frequency distribution of marks (out of 100) obtained by some students is shown.

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No.of students	3	5	7	10	12	15	12	6	2	8

Using the assumed-mean method, calculate the mean marks scored by a student.

Answer 1

Marks (Class intervals)	Class marks $\left(x_i\right)$	$$\begin{gathered} d_i=x_i-A \\ {d}_i=x_i-55 \end{gathered}$$	No. of students $\left(f_i\right)$	$\left(f_i\right)\left(d_i\right)$
0-10	5	$-$50	3	$-$150
10-20	15	$-$40	5	$-$200
20-30	25	$-$30	7	$-$210
30-40	35	$-$20	10	$-$200
40-50	45	$-$10	12	$-$120
50-60	$55\to A$	0	15	0
60-70	65	10	12	120
70-80	75	20	6	120
80-90	85	30	2	60
90-100	95	40	8	320
Total	-		$\sum _{}^{}{f}_i=80$	$\sum _{}^{}{f}_i{d}_i=-260$

$$\begin{gathered} \overline{d}=\frac{{\displaystyle \sum _{}^{}}{f}_i{d}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{-260}{80}=-3.25 \\ \mathrm{Mean}=\overline{x}=A+\overline{d} \\ =55+(-3.25) \\ =55-3.25 \\ =51.75 \end{gathered}$$

Mean marks scored by a student is 51.75.