Question

The monthly income of a group of 320 employees in a company is given below:

Monthly income (thousands)	No. of employees
6-7	20
7-8	45
8-9	65
9-10	95
10-11	60
11-12	30
12-13	5

Draw an ogive of the distribution on a graph paper taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph detemine: 

1. the median wage. 
2. number of employee whose income is below Rs. 8,500.
3. If salary of a senior employee is above Rs. 11,500, find the number of senior employee in the company. 
4. the upper quartile.

Answer 1

Monthly income (thousands)	No. of employees (f)	Cumulative frequency
6-7	20	20
7-8	45	65
8-9	65	130
9-10	95	225
10-11	60	285
11-12	30	315
12-13	5	320
Total	320

Number of employees = 320 

i. Median = `320/2` = 160^th term 

Through marks 160, draw a parallel line to x-axis which meets the curve at A. From A draw a perpendicular to x-axis meeting it at B. The value of point B is the median = Rs 9.3 thousands 

ii. The number of employees with income below Rs. 8500 = 95 (approx from the graph)

iii. Number of employees with income below Rs. 11500 = 305 (approx from the graph) 

Therefore number of employees with income (senior employees) = 320 - 305 = 15 

iv. Upper quartile = Q₃

= `320 xx 3/4`

= 240^th term

= 10.3 thousands

= Rs. 10,300