Question

Calculate the Arithmetic mean and median of the following frequency distribution:

Class Interval	10-20	20-40	40-70	70-120	120-200	Total
Frequency	4	10	26	8	2	50

Answer 1

Class Interval	f	X (Midpoint)	fX	c.f
10 – 20	4	15	60	4
20 – 40	10	30	300	14
40 – 70	26	55	1430	40
70 – 120	8	95	760	48
120 – 200	2	160	320	50
	$\sum f=50$		$\sum fX=2870$

Mean, $\overline{x}=\frac{\Sigma fX}{\Sigma f}=\frac{2870}{50}=57.4$

Median class is given by the size of the ${\frac{N}{2}}^{th}$ item,

i.e. the ${\frac{50}{2}}^{th}$ item, which is the 25^th item.

This corresponds to the class interval $40-70,$ so this is the median class.

Here, $N=50$

$\frac{N}{2}=25$

$l=$lower limit of the median class $=40$

$c.f=$ cumulative frequency of the preceding class

$f=$ frequency of the median class
Median $=l+\frac{\frac{N}{2}-c.f}{f}\times h$

$=40+\frac{25-14}{26}\times 30$

$=40+\frac{330}{26}=40+12.69=52.69$
Thus, the mean and median are $57.4$ and $52.69$ respectively.