Question

The following series relates to the daily income of workers employed in a firm. Compute minimum income earned by the top 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

Minimum income earned by top 25% of workers.

In order to calculate the minimum income earned by the top 25% of workers, we need to ascertain Q₃.

Class interval of Q₃ = `3(N/4)^{th}` item

= `3(65/4)^{th}` item

= 3 × 16.25^th item

= 48.75^th item

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

`Q_3 = L + ((3N)/4 - CF)/f xx i`

= `24.5 + ((3 xx 65)/4 - 30)/20 xx 5`

= `24.5 + (195/4 - 30)/20 xx 5`

= `24.5 + (48.75 - 30)/20 xx 5`

= Rs 29.187