Find out the airthmetic mean form the following data:
profit per shops:0-10 10-20 20-30 30-40 40-50 50-60
no.of shops:12 18 27 20 17 6?

Question

Find out the airthmetic mean form the following data:profit per shops:0-10 10-20 20-30 30-40 40-50 50-60no.of shops:12 18 27 20 17 6?

Answer

Calculating the Arithmetic Mean of Profit per Shops

Gather the Data: First, gather the data on profit per shops and the number of shops in each profit range. In this case, the data is as follows:
- Profit per shops: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
- Number of shops: 12, 18, 27, 20, 17, 6
Calculate the Midpoints: Find the midpoints of each profit range by taking the average of the lower and upper limits. The midpoints are as follows:
- 5, 15, 25, 35, 45, 55
Calculate the Product of Midpoints and Frequencies: Multiply each midpoint by the corresponding number of shops and sum the products. In this case, the calculations are as follows:
- (5*12) + (15*18) + (25*27) + (35*20) + (45*17) + (55*6) = 60 + 270 + 675 + 700 + 765 + 330 = 2800
Calculate the Total Number of Shops: Add up the total number of shops. In this case, the total number of shops is 100 (12+18+27+20+17+6).
Calculate the Arithmetic Mean: Divide the total product of midpoints by the total number of shops to find the arithmetic mean:
- Arithmetic Mean = 2800 / 100 = 28