Question

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

Monthly Income	No. of Employees
6000-7000	20
7000-8000	45
8000-9000	65
9000-10000	95
10000-11000	60
11000-12000	30
12000-13000	5

Draw an ogive the given distribution on a graph sheet taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph determine:
(1) the median wage
(2) the number of employees whose income is below Rs. 8500.
(3) if the salary of a senior employee is above Rs. 11,500, find the number of senior employees in the company.
(4) the upper quartile.

Answer 1

Monthly Income	No. of Employees	c.f.
6000-7000	20	20
7000-8000	45	65
8000-9000	65	130
9000-10000	95	225
10000-11000	60	285
11000-12000	30	315
12000-13000	5	320

Here, n = 320

1) Media  =  `n/2` th term = 160 th term

From the graph, the corresponding x coordinate is 9400

median wage = 9400 approx

2) The number of employees whose income is below Rs. 8500 = 95 (approx.)

3) The number of senior employees whose salary is above Rs. 11500 = 320 – 305 = 15 (approx.)

4) The upper quartile `Q_3 = ((3n)/4)^"th"` term = 240 th term

From the graph, the corresponding x co-ordinate is 10,300 (approx.)

Answer 2

Monthly	No. of Employees	c.f.
6000 - 7000	20	20
7000 - 8000	45	65
8000 - 9000	65	130
9000 - 10000	95	225
10000 - 11000	60	285
11000 - 12000	30	315
12000 - 13000	5	320

(i) From the graph, the median wage = 160·5 (appro.)
(ii) The number of employees whose income is below ₹8500 = 90 (appro.)
(iii) The number of senior employees whose salary is above ₹ 11500 = 20 (appro.)
(iv) The upper quartile Q₃ = 240 (appro.)