Question

Find the missing frequencies f₁ and f₂ in the table in given below, it is being given that the mean of the given frequency distribution is 50.

Class	0-20	20-40	40-60	60-80	80-100	Total
Frequency	17	f1	32	f2	19	120

Answer 1

Class	Frequency $\left(f_i\right)$	Mid values $\left(x_i\right)$	$(f_i\times x_i)$
0-20	17	10	170
20-40	f1	30	30 f1
40-60	32	50	1600
60-80	52- f1	70	3640-70 f1
80-100	19	90	1710
	$\sum f_i=120$		$\sum (f_i\times x_i)=7120-40f_1$

$$\begin{gathered} \text{We have:} \\ \text{17+}{f}_1+32+f_2+19=120 \\ \Rightarrow f_1+f_2=52 \\ \Rightarrow f_2=52-f_1 \\ \therefore \text{Mean,}\overline{x}=\frac{{\displaystyle \sum (f_i\times x_i)}}{{\displaystyle \sum f_i}} \\ \Rightarrow \text{50=}\frac{7120-40f_1}{120}[\because \text{Mean=50]} \\ \Rightarrow 40f_1=1120 \\ \therefore f_1=28 \\ \text{And}{f}_2=52-28 \\ \Rightarrow f_2\text{=24} \\ \therefore \text{The missing frequencies are}{f}_1=28\text{and}{f}_2\text{=24.} \end{gathered}$$