Question

The daily wages of 80 workers in a project are given below.

Wages (in Rs.)	400-450	450-500	500-550	550-600	600-650	650-700	700-750
No. of workers	2	6	12	18	24	13	5

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1. the median wage of the workers.
2. the lower quartile wage of workers.
3. the numbers of workers who earn more than Rs. 625 daily.

Answer 1

The cumulative frequency table of the given distribution is as follows:

Wages (in Rs.)	Upper limit	No. of workers	Cumulative frequency
400-450	450	2	2
450-500	500	6	8
500-550	550	12	20
550-600	600	18	38
600-650	650	24	62
650-700	700	13	75
700-750	750	5	80

The ogive is as follows:

Number of workers = n = 80

i. Median = `(n/2)^"th"` term = 40^th term

Through mark 40 on the Y-axis, draw a horizontal line which meets the curve at point A.

Through point A, on the curve draw a vertical line which meets the X-axis at point B

The value of point B on the X-axis is the median, which is 605.

ii. Lower quartile (Q₁) = `(80/4)^"th"` term = 20^th term = 550

iii. Through mark of 625 on X-axis, draw a verticle line which meets the graph at point C.

Then through point C, draw a horizontal line which meets the Y-axis at the mark of 50.

Thus, the number of workers that earn more than Rs. 625 daily = 80 – 50 = 30.