Question

Following is the distribution of the size of certain farms from a taluka (tehasil)
Find median size of farms.

Size of farm (in acres)	5 - 15	15 - 25	25 - 35	35 - 45	45 - 55	55 - 65	65 = 75
No. of farms	7	12	17	25	31	5	3

• A. $33.60$ Acres
• B. $37.60$ Acres
• C. $38.60$ Acres
• D. $40.60$ Acres

Answer 1

Answer: (D)

$40.60$ Acres

Consider the following table, to calculate median:

$ci$	$f_i$	$cf$
5-15	7	7
15-25	12	7+12=19
25-35	17	19+17=36
35-45	25	36+25=61
45-55	31	61+31=92
55-65	5	92+5=97
65-75	3	97+3=100

Median $=l+\frac{(\frac{N}{2}-cf)}{f_m}\times c$

Here,

Class Interval $c=10$

$N=\Sigma f_i=100$

$\frac{N}{2}=50$

$\Rightarrow$ Median class $=35-45$

$\Rightarrow$Frequency of median class$f_m=25$

Lower boundary of median class $l=35$

previous cumulative frequency of median class $cf=36$

$\therefore$ Median $=35+\frac{(\frac{100}{2}-36)}{25}\times 10$

$\therefore$ Median $=35+\frac{\left(14\right)}{25}\times 10$

$\therefore$ Median $=40.60$

Hence. option $D$ is correct.