Question

The rates of return on Cherry Jalopies, Inc., stock over the last five years were 19 percent, 11 percent, −1 percent, 3 percent, and 12 percent. Over the same period, the returns on Straw Construction Company’s stock were 16 percent, 20 percent, −4 percent, 3 percent, and 20 percent.

Calculate the variances and the standard deviations for Cherry and Straw. (Do not round intermediate calculations. Enter your variance as a decimal rounded to 5 decimal places. Enter your standard deviation as a percent rounded to 2 decimal places.)

	Cherry Straw Variance Standard deviation % %

Answer 1

Let us organize the data above in a table format and find out average return or mean.

	Cherry	Straw
Year 1	19%	16%
Year 2	11%	20%
Year 3	-1%	-4%
Year 4	3%	3%
Year 5	12%	20%
Mean	8.80000%	11.00000%

Standard Deviation (σ)= √[∑D²/N]

Where, D= Deviation of return from mean = Ri - X (Ri = return for year i and X = mean)

N = Total number of years =5

Using the above formula we get Standard Deviation as below for both stocks

Cherry	Straw
7.05408%	9.75705%

Variance = Square of Standard Deviation

or alternatively

Variance= ( Standard deviation)²= σ×σ

Using above formula we get Variance as below

Cherry	Straw
0.49760%	0.95200%