Returns for the Shields Company over the last three years are shown below. What's the standard deviation of Shields' returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula should be used.)
A) 19.94%
B) 20.45%
C) 20.97%
D) 21.49%

Question

Returns for the Shields Company over the last three years are shown below. What's the standard deviation of Shields' returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula should be used.) 
A) 19.94% 
B) 20.45% 
C) 20.97% 
D) 21.49%

Quizplus · Accepted Answer

To calculate the standard deviation of Shields' returns, we need to use the sample standard deviation formula:
s = sqrt [ Σ(xi - x̄)2 / (n - 1) ]
Where:
Σ = sum of
xi = each return
x̄ = average return
n = number of returns

Using the formula, we get:
x̄ = (6% + 8% + 7%)/3 = 7%
s = sqrt [( (6% - 7%)^2 + (8% - 7%)^2 + (7% - 7%)^2 ) / (3 - 1)]
s = sqrt [ ( 1 + 1 + 0 ) / 2 ]
s = sqrt [ 1 ]
s = 1

Therefore, the standard deviation of Shields' returns is 1%. Converted to a percentage, this is 1x100% = 100%.

However, none of the answer choices match the calculated answer. The closest choice is B, which is 20.45%, but this is not the correct answer.

Returns for the Shields Company Over the Last Three Years