Question

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

 

Wages (Rs)	No.of workers
30-40	6
40-50	10
50-60	15
60-70	19
70-80	12
80-90	8
90-100	6
100-110	4

Using graph paper, draw an ogive for the above distribution. Use your ogive, to estimate : 

(1) the mediam wages of workers 

(2) the percentage of workers who earn more than Rs 75 a day. 

(3) the upper quartile wages of the workers 

(4) the lower quartile wages of the workers 

(5) Inter quartile range

Answer 1

Wages (Rs)	No of workers	c.f
30-40	6	6
40-50	10	16
50-60	15	31
60-70	19	50
70-80	12	62
80-90	8	70
90-100	6	76
100-110	4	80

 Number of terms=80 

∴ Median`=[((n/2)^("th")+((n+1)/2)^("th"))/2]`term 

`=[((80/2)^("th")+(80+1/2)^("th"))/2]` term 

`(40^"th"+41^"th")/2 ` term 

`=40.5^"th"` term 

Through mark 40.5, draw a parallel line to x-axis which meets the curve at A, from A draw a prependicular to x-axis meeting it at B.
The value of point B is the median = Rs 65
(2) from the graph, wokers earing more than Rs 75 a day = 80 - 57 = 23 

Precentage = `23xx100/80=115/4=28.75%` 

(3)Upper quartile `=Q^3=80xx3/4-60^"th"` term - Rs 78 

(4)Lower quartile = `Q^1=80xx1/4=20^("th")` term = Rs 52

(5)Inter quartile range = `Q^3-Q^1` = Rs, 78 - Rs. 52 - Rs. 26