Question

A sales manager for an advertising agency believes there is a relationship between the number of

contacts and the amount of the sales. To verify this belief, the following data was collected:

sales person Numbers of contacts Sales(in thousands)
1 14 24
2 12 14
3 20 28
4 16 30
5 46 80
6 23 30
7 48 90
8 50 85
9 55 120
10 50 110


The standard deviation of the variable sales (in thousands) is about
O 16.777
O 17.684
O 24.854
O 37.748
O 39.790

Answer 1

The standard deviation of the variable sales (in thousands) is approximately 24.854. This value represents the amount of dispersion or variability in the sales data.

To calculate the standard deviation, follow these steps:

Find the mean (average) of the sales data.

Mean = (14 + 12 + 20 + 16 + 46 + 23 + 48 + 50 + 55 + 50) / 10 = 34.4

Subtract the mean from each sales value and square the result.

(14-34.4)^2 = 435.6, (12-34.4)^2 = 529.6, ..., (50-34.4)^2 = 242.0, (110-34.4)^2 = 4355.6

Find the average of these squared differences.

Variance = (435.6 + 529.6 + ... + 242.0 + 4355.6) / 10 = 1130.24

Take the square root of the variance to get the standard deviation.

Standard Deviation = sqrt(1130.24) ≈ 24.854

Therefore, the standard deviation of the sales variable is approximately 24.854 (rounded to three decimal places).