Question

The daily income of a sample of 50 employees are tabulated as follows:

Income (in Rs)	1 – 200	201 – 400	401 – 600	601 – 800
Number of employees	14	15	14	7

Find the mean daily income of employees.

Answer 1

Since, given data is not continuous, so we subtract 0.5 from the lower limit and add 0.5 in the upper limit of each class.

Now we first, find the class mark x_i of each class and then proceed as follows.

Income (in ₹)	Class marks `(bb(x_i))`	Number of employees `(bb(f_i))`	`bb(u_i = (x_i - a)/h = (x_i - 300.5)/200)`	`bb(f_iu_i)`
0.5 – 200.5	100.5	14	–1	–14
200.5 – 400.5	a = 300.5	15	0	0
400.5 – 600.5	500.5	14	1	14
600.5 – 800.5	700.5	7	2	14
		`N = sumf_i = 50`		`sumf_iu_i = 14`

∴ Assumed mean, a = 300.5

Class width, h = 200

And total observations, N = 50

By step deviation method,

Mean = `a + h xx 1/N xx sum_(i = 1)^5 f_iu_i`

= `300.5 + 200 xx 1/50 xx 14`

= 300.5 + 56

= 356.5

Hence, the mean daily income of employees is ₹ 356.5.