Question

A sample of 5 months of sales data provided the following information: Month 1 2 3 4 5 Units Sold 97 110 88 97 93

a. Develop a point estimate of the population mean number of units sold per month (to 1 decimal).

b. Develop a point estimate of the population standard deviation (to 2 decimals).

Answer 1

a) n = Number of Data Values = 5

Sum of Data Values = Σxᵢ = 485

Sample Mean = x̄ = Σxᵢ / n = 485 / 5 = 97

population mean number of units sold per month is 97

b)

Data (x)   Deviation From Mean = x - x̄   Square of Deviation = (x - x̄)²  
x = 88 (88) - (97) = 9 (9)² = 81  
x = 93 (93) - (97) = 4 (4)² = 16  
x = 97 (97) - (97) = 0 (0)² = 0  
x = 97 (97) - (97) = 0 (0)² = 0  
x = 110   (110) - (97) = -13    (-13)² = 169

Sum of deviation squared = Σ(x_i - x̄)² = 266          (Sum of values in third column)

s² = Sample Variance = Σ(x_i - x̄)²/(n - 1) = 266/4 = 66.5

s = Sample Standard Deviation = √ Sample Variance = √66.5 = 8.15

point estimate of the population standard deviation is 8.15