Question

Look at the frequency distribution table given below:

Class interval	35-45	45-55	55-65	65-75
Frequency	8	12	20	10

The median of the above distribution is
(a) 56.5
(b) 57.5
(c) 58.5
(d) 59

Answer 1

(b) 57.5

$\mathrm{Class}\mathrm{}\mathrm{interval}$	$35-45$	$45-55$	$55-65$	$65-75$
$\mathrm{Frequency}$	$8$	$12$	$20$	$10$
$\mathrm{Cumulative}\mathrm{}\mathrm{frequency}$	$8$	$20$	$40$	$50$

$$\begin{gathered} \mathrm{Here},N=50 \\ \Rightarrow \frac{N}{2}=25,whichliesintheclassintervalof55-65. \\ \mathrm{Now},cf=55,f=20\mathrm{and}l=50 \\ \therefore \mathrm{Median}=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ =50+\frac{65-55}{20}\times \left(25-20\right) \\ =57.5 \end{gathered}$$