The following are distances (in miles) traveled to the workplace by 5 employees of a certain brokerage firm. \[ 11,9,29,15,1 \] Send data to calculator Find the standard deviation of this sample of distances. Round your answer to two decimal places. (If necessary, consult a list of formulas.) Explanation Recheck
Solution
Step 1 ：The given distances (in miles) traveled to the workplace by 5 employees of a certain brokerage firm are 11, 9, 29, 15, 1.
Step 2 ：To find the standard deviation of a sample, we first need to find the mean (average) of the sample.
Step 3 ：The mean of the given distances is \( \frac{11+9+29+15+1}{5} = 13.0 \) miles.
Step 4 ：Next, for each number in the sample, we subtract the mean and square the result. The squared differences are \( (11-13)^2, (9-13)^2, (29-13)^2, (15-13)^2, (1-13)^2 \).
Step 5 ：The next step is to find the mean of these squared differences. This is called the variance. The variance is \( \frac{(11-13)^2 + (9-13)^2 + (29-13)^2 + (15-13)^2 + (1-13)^2}{5} = 106.0 \).
Step 6 ：Finally, we take the square root of the variance to get the standard deviation. The standard deviation is \( \sqrt{106.0} = 10.3 \).
Step 7 ：The standard deviation of the sample of distances is \(\boxed{10.3}\) miles.
