Question

Size of the agriculture holding in a survey of 200 families is given in the following table:

Size of Agriculture	0-5	5-10	10-15	15-20	20-25	25-30	30-35
Number of family	10	15	30	80	40	20	5

Complete median and mode size of the holdings.

Answer 1

$SizeofAgriculture$	$No.offamily$	$c.f$
$0-5$	$10$	$10$
$5-10$	$15$	$25$
$10-15$	$30$	$55$
$15-20$	$80$	$135$
$20-25$	$40$	$175$
$25-30$	$20$	$195$
$30-35$	$5$	$200$
	$N=200$

Here, $N=200$ then, $\frac{200}{2}=100$

$\therefore$ Median class $=15-20$

We have, $l=15,c.f=55,f=80,h=5$

$Median=l+\frac{\frac{N}{2}-c.f}{f}\times h$

$=15+\frac{100-55}{80}\times 5$

$=15+\frac{45}{80}\times 5$

$=15+2.81$

$=17.81$

Here, modal class $=15-20$

We have, $f_0=30,f_1=80,f_2=40,h=5$

$\Rightarrow$ $Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

$=15+\frac{80-30}{2\times 80-30-40}\times 5$

$=15+0.55$

$=15.55$