Question

The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% 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	5

(Hint: Compute median, lower quartile and upper quartile)

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

(a) Highest income of lowest 50% workers

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

(b) Minimum income earned by top 25% workers
In order to calculate the minimum income earned by top 25% workers, we need to ascertain Q₃.

48.75^th item lies in 50^th item and the corresponding class interval is 24.5 – 29.5.

(c) Maximum income earned by lowest 25% workers
In order to calculate the maximum income earned by lowest 25% workers, we need to ascertain Q₁.

16.25^th item lies in the 30^th cumulative frequency and the corresponding class interval is 19.5 – 24.5