Question

The daily income of a sample of 50 employees are tabulated as follows:
Income (in ₹): 1-200 201-400 401-600 601-800

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	${\mathit{u}}_{\mathbf{i}}\mathbf{=}\frac{{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{500}\mathbf{.}\mathbf{5}}{\mathbf{200}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
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		$\sum _{}{f}_i{u}_i=-36$

We know that mean,
Now, we have $N=\sum _{}{f}_i=50,h=200,A=500.5,\sum _{}{f}_i{u}_i=-36$
$$\begin{gathered} \overline{X}=500.5+200\left[\frac{1}{50}\times \left(-36\right)\right] \\ =500.5-144 \\ =356.5 \end{gathered}$$