The standard deviation of the past five monthly returns for K and Company are 4.25 percent, 4.13 percent, -102.05 percent, 3.25 percent, and 7.75 percent. What is the standard deviation?
A)1.40 percent
B)3.37 percent
C)3.53 percent
D)16.83 percent

Question

Quizplus · Accepted Answer

To calculate the standard deviation, we need to first calculate the variance by squaring each of the monthly returns, adding them up, dividing by the total number of returns, and then subtracting the square of the mean return. 
Variance = [(0.0425)^2 + (0.0413)^2 + (0.0205)^2 + (0.0325)^2 + (0.0775)^2]/5 - [(0.0425 + 0.0413 + 0.0205 + 0.0325 + 0.0775)/5]^2
Variance = 0.001477 - 0.001379 = 0.000098
Standard deviation = square root of the variance = square root of 0.000098 = 0.00353 or 3.53% 
Therefore, the answer is C.

The Standard Deviation of the Past Five Monthly Returns for K