Question

If the median of the following frequency distribution is 46, find the missing frequencies.

Variable:	10-20	20-30	30-40	40-50	50-60	60-70	70-80	Total
Frequency:	12	30	?	65	?	25	18	229

Answer 1

Let the frequency of the class $30-40$ be $f_1$ and that the class of the class $50-60$ be $f_2$. The total frequency is 229.
$12+30+f_1+65+f_2+25+18=229\Rightarrow f_1+f_2=79$
It is given that the median is $46.$
Clearly, 46 lies in the class $40-50$. So, $40-50$ is the median class.
$\therefore l=40,h=10,f=65$ and $F=12+30÷f_1=42+f_1,N=229$
Now, $Median=l+\frac{\frac{N}{2}-F}{f}\times h$
$\Rightarrow 46=40+\frac{\frac{229}{2}-(42+f_1)}{65}\times 10$
$\Rightarrow 46=40+\frac{145-2f_1}{13}$
$\Rightarrow 6=\frac{145-2f_1}{13}\Rightarrow 2f_1=67\Rightarrow f_1=33.5$ or $34$ (say)
Since $f_1+f_2=79$. Therefore,$f_2=45$.
Hence, $f_1=34$ and $f_2=45.$