Question

The following series relates to the daily income of workers employed in a firm. Compute the highest income of the lowest 50% of workers.

Daily Income (in Rs)	10-14	15-19	20-24	25–29	30-34	35-39
Number of workers	5	10	15	20	10	2

Answer 1

Daily Income (in Rs) Class Interval	No. of Workers (f)	Cumulative frequency  (CF)
9.5 - 14.5	5	5
14.5 - 19.5	10	15
19.5 - 24.5	15	30
24.5 - 29.5	20	50
29.5 - 34.5	10	60
34.5 - 39.5	5	65
	∑f = 65

Highest income of lowest 50% workers

∑f = N = 65

Median class = Size of `(N/2)^"th"` item

= Size of `(65/2)^"th"` item = 32.5^th item

32.5^th item lies in the 50^th cumulative frequency and the corresponding class interval is 24.5 - 29.5.

Median = `L + (N/2 - CF)/f xx i`

= `24.5 + (32.5 - 30)/20 xx 5`

= `24.5 + 2.5/20 xx 5`

= Rs 25.125