A portfolio's annual total returns (in percent)for a 5-year period are: The median and the standard deviation for this sample are closest to:
A)Option A
B)Option B
C)Option C
D)Option D

Question

A portfolio's annual total returns (in percent)for a 5-year period are:  The median and the standard deviation for this sample are closest to: 
A)Option A 
B)Option B 
C)Option C 
D)Option D

Quizplus · Accepted Answer

The median is the middle value when the data is arranged in order. In this case, we have five values:
11, 8, 13, 10, 12
Arranging them in order:
8, 10, 11, 12, 13
The middle value is 11.

The formula for standard deviation of a sample is:
s = sqrt [ Σ ( xi - x̄ )2 / ( n - 1 ) ]
where xi is the ith value, x̄ is the sample mean, and n is the sample size.

Using this formula, we get:
x̄ = (11+8+13+10+12)/5 = 10.8
Σ ( xi - x̄ )2 = (11-10.8)2 + (8-10.8)2 + (13-10.8)2 + (10-10.8)2 + (12-10.8)2 = 9.6
s = sqrt (9.6/4) = 1.549
So the closest choice is C.

A Portfolio's Annual Total Returns (In Percent)for a 5-Year Period