Question

The mean of the following frequency distribution is 57.6 and the sum of the observations is 50

Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	7	f1	12	f2	8	5

Answer 1

Class	Frequency $\left(f_i\right)$	Mid values $\left(x_i\right)$	$(f_i\times x_i)$
0-20	7	10	70
20-40	f1	30	30 f1
40-60	12	50	600
60-80	18- f1	70	1260-70 f1
80-100	8	90	720
100-120	5	110	550
	$\sum f_i=50$		$\sum (f_i\times x_i)=3200-40f_1$

$$\begin{gathered} \text{We have:} \\ \text{7+}{f}_1+12+f_2+8+5=50 \\ \Rightarrow f_1+f_2=18 \\ \Rightarrow f_2=18-f_1 \\ \therefore \text{Mean,}\overline{x}=\frac{{\displaystyle \sum (f_i\times x_i)}}{{\displaystyle \sum f_i}} \\ \Rightarrow \text{57}\text{.6=}\frac{3200-40f_1}{50}[\because \text{Mean=57}\text{.6}] \\ \Rightarrow 40f_1=320 \\ \therefore f_1=8 \\ \text{And}{f}_2=18-8 \\ \Rightarrow f_2\text{=10} \\ \therefore \text{The missing frequencies are}{f}_1=8\text{and}{f}_2\text{=10.} \end{gathered}$$