Question

Number of persons living in a house is reported to be as under 500 houses in a village. Find the median number of persons in a house in the village.

Number of Persons in a House	1	2	3	4	5	6	7	8	9	10
Number of Houses	26	113	120	95	60	42	21	14	5	4

Answer 1

No. of Persons in a House	No. of Houses (f)	Cumulative Frequency (c.f.)
1 2 3 4 5 6 7 8 9 10	26 113 120 95 60 42 21 14 5 4	26 139 259 354 414 456 477 491 496 500
	∑f = 500

Median = size of ${\left(\frac{N+1}{2}\right)}^{th}$item
or, Median = size of ${\left(\frac{500+1}{2}\right)}^{th}$ item
or, Median = size of 250.5^th item
Now, we need to locate this item in the column of Cumulative Frequency. The item just exceeding 250.5^th is 259 (in the c.f. column), which is corresponding to 3.
Hence, median is 3.