Question

Consider the data

$\begin{array}{cccccccc}\text{Class}& 65-85& 85-105& 105-125& 125-145& 145-165& 165-185& 185-205\\ \text{Frequency}& 4& 5& 13& 20& 14& 7& 4\end{array}$

The difference of the upper limit of the median class and the lower limit of the modal calss is
(a) $0$
(b) $19$
(c) $20$
(d) $38$

Answer 1

Given data is,

$\begin{array}{cccccccc}\text{Class}& 65-85& 85-105& 105-125& 125-145& 145-165& 165-185& 185-205\\ \text{Frequency}& 4& 5& 13& 20& 14& 7& 4\end{array}$

Here, Sum of the frequencies is

$N=4+5+13+20+14+7+4=67$

$\Rightarrow \frac{N}{2}=\frac{67}{2}=33.5$

which lies in the interval $125-145$.
Hence, upper limit of median calss is 145.
Here, we see that the highest frequency is $20$

which lies in $125-145$.

Hence, the lower limit of modal class is $125$.
$\therefore$ Required difference $=$Upper limit of median class$-$Lower limit of modal class

$=145-125$

$=20$

Hence, Option C is correct.