Question

The mean of the followlng frequency table is $53$. But the frequencies $f_1$ and $f_2$ in the classes $20-40$ and $60-80$ are missing. Find the missinq frequencies.

Age (in years)	0-20	20-40	40-60	60-80	80-100	Total
No. of people	15	$f_1$	21	$f_2$	17	100

• A. $f_1=20,f_2=28$
• B. $f_1=17,f_2=19$
• C. $f_1=19,f_2=25$
• D. $f_1=18,f_2=29$

Answer 1

The correct option is D $f_1=18,f_2=29$

Answer:-

Age	No. of people (f)	$x_i=\frac{\text{lower limit + upper limit}}{2}$	$x_i{f}_i$
0-20	15	10	150
20-40	$f_1$	30	$30f_1$
40-60	21	50	1050
60-80	$f_2$	70	$70f_2$
80-100	17	90	1530

$\Sigma f_i=53+f_1+f_2$

$\Sigma f_i.x_i=2730+30f_1+70f_2$

Given:- $\Sigma f_i=100$

$\Rightarrow 53+f_1+f_2=100$

$\Rightarrow f_1+f_2=100-53$

$\Rightarrow f_1+f_2=47⟶eq.\left(i\right)$

Given:- Mean = $\frac{\Sigma x_i.f_i}{\Sigma f_i}=53$

$\Rightarrow \frac{2730+f_1+f_2}{100}=53$

$\Rightarrow 273+f_1+f_2=530$

$f_1+f_2=257⟶eq.\left(ii\right)$

from eq. (i) $\&$ (ii), we get

$f_1=18,f_2=29$

$\Rightarrow f_1=18,f_2=29$