Question

If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies.

$\begin{array}{cccccc}\text{Marks}& 0-10& 10-30& 30-60& 60-80& 80-90\\ \text{Number of students}& 5& f_1& 30& f_2& 2\end{array}$

[3 Marks]

Answer 1

$\begin{array}{cccccc}\text{Marks}& 0-10& 10-30& 30-60& 60-80& 80-90\\ \text{Number of students}& 5& f_1& 30& f_2& 2\end{array}$

$\because$ Total frequency = 60 [given]
$\therefore 5+f_1+30+f_2+2=60$
$\Rightarrow 37+f_1+f_2=60$
$\Rightarrow f_1+f_2=23$ ...(i)
[0.5 Marks]

Now, N = 60
$\therefore \frac{N}{2}=30$
and median = 40
Since, it lies in the class interval 30-60
So, 30-60 is the median class.
[0.5 Marks]

Here, $l=30,h=30,f=30,cf=5+f_1,n=60$
$\therefore \text{Median}=l+\frac{\frac{n}{2}-cf}{f}\times h$ [1 Mark]
$\Rightarrow 40=30+\frac{30-5-f_1}{30}\times 30$
$\Rightarrow 40=30+25-f_1$
$\Rightarrow 40=55-f_1\Rightarrow f_1=15$
$\Rightarrow f_2=23-15$
$and{f}_2=23-15$ [from Eq. (i)]
= 8
[1 Mark]