Over the past ﬁve years, Redstone Enterprises produced returns of 31%, 38%, -41%, 8%, and 15%. The mean of these returns is _____% and the standard deviation is _____%.

Question

Quizplus · Accepted Answer

To find the mean of the returns, we add up all the returns and divide by the number of returns:
(31 + 38 - 41 + 8 + 15) / 5 = 10.2%

To find the standard deviation, we first need to find the variance:
1. Calculate the mean return:
(31 + 38 - 41 + 8 + 15) / 5 = 10.2%
2. Calculate the difference between each return and the mean:
31 - 10.2 = 20.8
38 - 10.2 = 27.8
-41 - (-10.2) = -30.8
8 - 10.2 = -2.2
15 - 10.2 = 4.8
3. Square each difference:
20.8^2 = 433.44
27.8^2 = 772.84
(-30.8)^2 = 948.64
(-2.2)^2 = 4.84
4.8^2 = 23.04
4. Add up all the squared differences:
433.44 + 772.84 + 948.64 + 4.84 + 23.04 = 2182.8
5. Divide by the number of returns minus 1 (this is called the sample variance):
2182.8 / (5 - 1) = 545.7
6. Take the square root of the sample variance to get the standard deviation:
sqrt(545.7) = 31.04%

Therefore, the answer is B.

Over the Past ﬁVe Years, Redstone Enterprises Produced Returns of 31