Question

The daily expenses of 40 families has been shown by the following frequency distribution:

Expenses (in ₹)	500 − 700	700 − 900	900 − 1100	1100 − 1300	1300 − 1500
Number of families	6	8	10	9	7

Find the mean daily expenses.

Answer 1

Here, h = 200

Let the assumed mean, A be ₹1000.

Expenses (in ₹)	Mid-Values(xi)	Number of Families(fi)	${\mathit{d}}_i\mathbf{=}{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{1000}$	${\mathit{u}}_i\mathbf{=}\frac{{\mathit{x}}_i\mathbf{-}\mathbf{1000}}{\mathbf{200}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
500−700	600	6	−400	−2	−12
700−900	800	8	−200	−1	−8
900−1100	1000	10	0	0	0
1100−1300	1200	9	200	1	9
1300−1500	1400	7	400	2	14
		$\underset{}{\sum f_i=40}$			$\underset{}{\sum f_i{u}_i=3}$

We know

Mean $=A+h\times \left(\frac{\sum _{}{f}_i{u}_i}{\sum _{}{f}_i}\right)$

∴ Mean daily expenses

$$\begin{gathered} =1000+200\times \left(\frac{3}{40}\right) \\ =1000+15 \\ =₹1015 \end{gathered}$$

Thus, the mean daily expenses is ₹1015.