Question

Find the mean, using assumed-mean method:

Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	20	35	52	44	38	31

Answer 1

Class	Frequency $\left(f_i\right)$	Mid Values$\left(x_i\right)$	Deviation $\left(d_i\right)$ $d_i=\left(x_i-50\right)$	$(f_i\times d_i)$
0-20	20	10	-40	-800
20-40	35	30	-20	-700
40-60	52	50=A	0	0
60-80	44	70	20	880
80-100	38	90	40	1520
100-120	31	110	60	1860
	$\sum f_i=220$			$\sum (f_i\times d_i)=2760$

$$\begin{gathered} \text{Let}A=50\text{be the assumed mean}\text{. Then we have:} \\ \mathrm{Now},\mathrm{m}\text{ean,}\overline{x}=A+\frac{{\displaystyle \sum (f_i\times d_i)}}{{\displaystyle \sum f_i}} \\ \text{=50+}\frac{2760}{220} \\ \text{=50+12}\text{.55} \\ \therefore \overline{x}=62.55 \end{gathered}$$