Question

Calculate the median from the following data:

Rent In Rs.	15-25	25-35	35-45	45-55	55-65	65-75	75-85	85-95
No. of Houses	$8$	$10$	$15$	$25$	$40$	$20$	$15$	$7$

Answer 1

Rent (in Rs.) (x)	No. of houses (f)	C.F.
15-25	8	8
25-35	10	18
35-45	15	33
45-55	25	58
55-65	40	98
65-75	20	118
75-85	15	133
85-95	7	140
	N = 140

As, $N=140\Rightarrow \frac{N}{2}=\frac{140}{2}=70$

As $98$ is just greater than $70$, therefore median class is $55-65$.

$\text{Median}=l+\frac{\frac{N}{2}+C}{f}\times h$

Here, $l=$ lower limit of median class $=55$

$C=C.F.$ of the class preceding the median class $=58$

$h=$ higher limit - lower limit $=65-55=10$

$f=$frequency of median class $=40$

$\therefore \text{Median}=55+\frac{70-58}{40}\times 10=55+3=58$