Question

The daily wages of 160 workers in a building project are given below:

Wages in ₹	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
No. of Workers	12	20	30	38	24	16	12	8

Using a graph paper, draw in Ogive for the above distribution.
Use your Ogive to estimate :
(i) the median wage of the workers.
(ii) the upper quartile wage of the workers
(iii) the lower quartile wages of the workers
(iv) the percentage of workers who earn more than ₹ 45 a day.

Answer 1

Wages (in ₹)	No. of Workers	Cummulative frequency
0 - 10	12	12
10 - 20	20	32
20 - 30	30	62
30 - 40	38	100
40 - 50	24	124
50 - 60	16	140
60 - 70	12	152
70 - 80	8	160

(i) Median = `("n"/2)^"th"` observation
= `(160/2)^"th"` observation
= 80^th observation
Now the 80^th position in the ogive diagram represent the median wage of workers by the graph = 35.
(ii) Upper quartile = `((3"n")/(4))^"th"` observation
= `((3 xx 160)/(4))^"th"` observation
= 120^th observation
(iii) Lower quartile = `("n"/4)^"th"` observation
= `(160/4)^"th"` observation
40^th observation
The 40^th observation in the ogive diagram represents wage of the workers Q₁ = 23·5
(iv) The percentage of workers earmore than ₹45
= `(160 - 115)/(100) xx 100`
= `(45 xx 10)/(16)`
= 28·125%.