Over the past six years, a stock had annual returns of 18 percent, - 6 percent, 2 percent, 27 percent, - 11 percent, and 13 percent, respectively. What is the standard deviation of these returns?

Question

Trenton Browning

Business

17 July, 18:02

Over the past six years, a stock had annual returns of 18 percent, - 6 percent, 2 percent, 27 percent, - 11 percent, and 13 percent, respectively. What is the standard deviation of these returns?

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Answers (1)

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Moriah Whitney · Answer 1

13.38%

Explanation:

Step 1: find the mean

(18% - 6% + 2% + 27% - 11% + 13%) / 6 = 43% / 6 = 7.17%

Step 2: for each number subtract the mean and square the result

(18% - 7.17%) ² = 117.36

(-6% - 7.17%) ² = 173.36

(2% - 7.17%) ² = 26.69

(27% - 7.17%) ² = 393.36

(-11% - 7.17%) ² = 330.03

(13% - 7.17%) ² = 34.03

Step 3: calculate the mean of the squared differences

(117.36 + 173.36 + 26.69 + 393.36 + 330.03 + 34.03) / 6 = 1,074.83 / 6 = 179.14

Step 4: calculate the square root of step 3

√179.14 = 13.38%