Question

Find out the mean profits from the following frequency distribution

Profit per shop (in Rs)	Number of shops $\left(f_i\right)$
100 - 200	10
200 - 300	18
300 - 400	20
400 - 500	26
500 - 600	30
600 - 700	28
700 - 800	18

Answer 1

Calculation of Mean

Profit (in Rs)	No. of shops $\left(f_i\right)$	Mid-point $\left(x_i\right)$	Deviation $d_i=x_i-450$	$f_i{d}_i$
100 - 200	10	150	-300	-300
200 - 300	18	250	-200	-3600
300 - 400	20	50	-100	-2000
400 - 500	26	70	0	0
500 - 600	30	90	100	3000
600 - 700	30	90	100	5600
600 - 800	18	750	300	5400
	150			5400

Hence by assumed mean method
$\overline{x}=a+\frac{1}{n}\sum _{i=l}^k{f}_i{d}_i=450+\frac{5400}{150}$
= 450 + 36 = 486
Therefore mean profit is Rs 486