Question

Given the following frequency distribution with some missing frequencies
$\begin{array}{cccccccc}\text{Class}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 180& & 34& 180& 136& & 50\end{array}$
If the total frequency is $685$ and approximate value of median is $42.6$, then the approximate values for missing frequencies are

• A. $87,23$
• B. $80,25$
• C. $82,24$
• D. $83,22$

Answer 1

The correct option is C $82,24$

Let missing frequincies be $x,y$
$\begin{array}{cccccccc}\text{class}& 10-20& 20-30& 30-30& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 180& x& 34& 180& 136& y& 50\\ \text{C.F}& 180& 180+x& 214+x& 394+x& 530+x& 530+x+y& 580+x+y\end{array}$
Given: $580+x+y=685\Rightarrow x+y=105\cdots \left(1\right)$
Now,
$\frac{N}{2}=\frac{685}{2}=342.5$
$\text{Median}=l+\left(\frac{\left(\frac{N}{2}\right)-F}{f}\right)\times h$
Here, Median class is $40-50$
$l=\text{lower limit of median class}=40$
$N=\text{total frequency}=685$
$F=\text{C.F of class just preceeding median class}=214+x$
$f=\text{frequency of median class}=180$
$h=\text{width of median class}=10$
putting these values in above equation
$42.6=40+\frac{(342.5-214-x)}{180}\times 10$
$\Rightarrow x=81.7$
$\therefore y=105-81.7=23.3$
As frequencies are always whole numbers ,
$\therefore$ missing frequencies are $82,24$