Question

A process is measuring the number of returns per 100 receipts at a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, 11. Find the standard deviation of this sampling distribution.

Answer 1

Answer:

The standard deviation of this sampling distribution is 3.07

Explanation:

There are n = 10 samples

Mean: $\frac{\sum x_{i}}{n}$ = (10 + 9 + 11 + 7 + 3 + 12 + 8 + 4 + 6 + 11) / 10 = 8.1

Variance: s^2 = $\frac{\sum {(x_{i} - mean)^{2}}}{n-1}$

= [(10 - 8.1)^2 + (9 - 8.1)^2 + (11 - 8.1)^2 + (7 - 8.1)^2+ (3 - 8.1)^2+ (12 - 8.1)^2] + (8 - 8.1)^2+ (4 - 8.1)^2+ (6 - 8.1)^2+ (11 - 8.1)^2] / 9

= 9.43

Standard deviation: s = $\sqrt{s^2}$ = $\sqrt{9.43}$ = 3.07