Question

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

Income (in Rs.):	1-1200	201 -400	401-600	601 - 800
No.of employees :	14	15	14	7

Find the mean daily income of employees.

Answer 1

Let the assumed mean A = 500.5 and h = 200.

Marks	Mid-Value(xi)	Frequency	\[u_i = \frac{x_i - 500 . 5}{200}\]	\[f_i u_i\]
1–200	100.5	14	-2	-28
201–400	300.5	15	-1	-15
401–600	500.5	14	0	0
601–800	700.5	7	1	7
		N = 50		`sumf_iu_i = -36`

We know that mean,   `overlineX = A +h (1/N sumf_iu_i)`

Now, we have

\[N = \sum_{} f_i = 50, h = 200, A = 500 . 5, \sum_{} f_i u_i = - 36\]

\[\bar{X} = 500 . 5 + 200\left[ \frac{1}{50} \times \left( - 36 \right) \right]\]

\[ = 500 . 5 - 144\]

\[ = 356 . 5\]