Question

The following data shows the number of family members living in different bungalows of a locality:

Number of Members	0 − 2	2 − 4	4 − 6	6 − 8	8 − 10	Total
Number of Bungalows	10	p	60	q	5	120

If the median number of members is found to be 5, find the values of p and q.

Answer 1

Median = 5

Total number of bungalows = 120

Number of Members	f	x	c.f
0 − 2	10	1	10
2 − 4	p	3	10 + p
4 − 6	60	5	70 + p
6 − 8	q	7	70 + p + q
8 − 10	5	9	75 + p + q
	`sumf = 120` = 75 + p + q

75 + p + q = 120

p + q = 120 − 75

p + q = 45   ...(i)

Median = 5

Median class = 4 – 6

l = 4, c.f. = 10 + p, h = 2, f = 60

Median = `l + ((n/2 - c.f.))/f xx h`

`5 = 4 + (120/2 - (10 + p))/60 xx 2`

`5 = 4 + (60 - 10 - p)/60 xx 2`

`5 = 4 + (50 - p)/60 xx 2`

`5 = 4 + (100 - 2p)/60`

`5 − 4 = (100 - 2p)/60`

`1 = (100 - 2p)/60`

60 = 100 − 2p

2p = 100 − 60

2p = 40

p = `40/2`

p = 20

Put the value p in equation (i),

20 + q = 45

q = 45 − 20

q = 25