Question

Find the mean, using assumed-mean method:

Class	0-40	40-80	80-120	120-160	160-200
Frequency	12	20	35	30	23

Answer 1

Class	Frequency $\left(f_i\right)$	Mid values$\left(x_i\right)$	Deviation $\left(d_i\right)$ $\left(d_i\right)=\left(x_i-100\right)$	$(f_i\times d_i)$
0-40	12	20	-80	-960
40-80	20	60	-40	-800
80-120	35	100=A	0	0
120-160	30	140	40	1200
160-200	23	180	80	1840
	$\sum f_i=120$			$\sum (f_i\times d_i)=1280$

$$\begin{gathered} \text{Let}A=100\text{be the assumed mean}\text{. Then we have:} \\ \text{Mean,}\overline{x}=A+\frac{{\displaystyle \sum (f_i\times d_i)}}{{\displaystyle \sum f_i}} \\ \text{= 100+}\frac{1280}{120} \\ \text{=100+10}\text{.67} \\ \therefore \overline{x}=110.67 \end{gathered}$$