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

• A. $58$
• B. $61$
• C. $59$
• D. $63$

Answer 1

The correct option is A $58$

Rent	No. of houses	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
	$\Sigma f_i=140$

$\frac{N}{2}=\frac{140}{2}=70$

$\Rightarrow \text{98 is just greater than 70}\therefore \text{Median class is 55-65.}$

Median $=L+\frac{\frac{N}{2}-C}{f}\times w$

L = Lower limit of median class $=55$

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

f = frequency of median class $=40$

w = width of median class $=65-55=10$

Median $=55+\frac{70-58}{40}\times 10=55+\frac{12}{4}=58$

A) 58