A portfolio's annual total returns (in percent)for a five-year period are: -7.14 1.62 2.50 -2.50 9.27.
The median and the standard deviation for this sample are the closest to ______________.
A) 0.75 and 5.46
B) 1.62 and 5.46
C) 1.62 and 6.11
D) 2.50 and 6.11

Question

Quizplus · Accepted Answer

The median is the middle value in a set of data, so we need to order the returns from lowest to highest: 
-7.14, -2.50, 1.62, 2.50, 9.27. The middle value is 1.62, so that is the median. 
To calculate the standard deviation, we first need to find the mean return: 
(-7.14 + 1.62 + 2.50 - 2.50 + 9.27) / 5 = 0.95. 
Then, we calculate the deviation of each return from the mean: 
-8.09, 0.67, 1.55, -3.45, 8.32. 
We square each deviation and sum them: 
(-8.09)^2 + 0.67^2 + 1.55^2 + (-3.45)^2 + 8.32^2 = 120.22. 
Dividing by 4 (since we have 5 returns, we need to subtract 1 from the sample size) and taking the square root gives us the standard deviation: 
sqrt(120.22/4) = 6.11. 
Therefore, the closest answer choice is C: 1.62 and 6.11.

A Portfolio's Annual Total Returns (In Percent)for a Five-Year Period