Question

Find the mean, using assumed-mean method:

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of students	12	18	27	20	17	6

Answer 1

Class	Frequency $\left(f_i\right)$	Mid values$\left(x_i\right)$	Deviation $\left(d_i\right)$ $d_i=\left(x_i-25\right)$	$(f_i\times d_i)$
0-10	12	5	-20	-240
10-20	18	15	-10	-180
20-30	27	25=A	0	0
30-40	20	35	10	200
40-50	17	45	20	340
50-60	6	55	30	180
	$\sum f_i=100$			$\sum (f_i\times d_i)=300$

$$\begin{gathered} \text{Let}A=25\text{be the assumed mean}\text{. Then we have:} \\ \text{Mean,}\overline{x}=A+\frac{{\displaystyle \sum (f_i\times d_i)}}{{\displaystyle \sum f_i}} \\ \text{= 25+}\frac{300}{100} \\ \text{=28} \\ \therefore \overline{x}=28 \end{gathered}$$