Question

The following series relates to the daily income of workers employed in a firm. Compute maximum income earned by the lowest 25% 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

Maximum income earned by lowest 25% of workers.

In order to calculate the maximum income earned by the lowest 25% of workers, we need to ascertain Q_1.

Class interval of Q₁ = `(N/4)^{th}` items

= `(65/4)^{th}` item = 16.25^th item

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

`Q_1 = L + (N/4 - CF)/f xx i`

= `19.5 + (16.25 - 15)/15 xx 5`

= `19.5 + 1.25/15 xx 5`

= Rs 19.92