Question

The following is the distribution of the size of certain farms from a taluka (tehasil):

Size of Farms (in acres)	Number of Farms
5 – 15	7
15 – 25	12
25 – 35	17
35 – 45	25
45 – 55	31
55 – 65	5
65 – 75	3

Find median size of farms.

Answer 1

Calculation of the Median size of farms.

Size of Farms (in acres)	f	cf
5 – 15	7	7
15 – 25	12	19
25 – 35	17	36
35 – 45	25	61
45 – 55	31	92
55 – 65	5	97
65 – 75	3	100

We have N=100 ⇒ N/2=50

The cumulative frequency just greater than N/2 is 61 and the corresponding class is 35-45.
Thus, 35-45 is the median class such that l =35, f =25, cf =36,h =10.

`Median=l+(N/2-cf)/fxxh`

`=35+(50-36)/25xx10`

`=35+5.6`

`=40.6`