Question

Check my work The rates of return on Cherry Jalopies, Inc., stock over the last five years were 16 percent, 11 percent. -1 percent, 6 percent, and 11 percent. Over the same period, the returns on Straw Construction Company's stock were 16 percent, 23 percent, -6 percent, 6 percent, and 11 percent. points 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.) Skipped Cherry Straw eBook Variance Standard deviation Print

Answer 1

Year	Return on Cherry	Return on Straw
1	16%	16%
2	11%	23%
3	-1%	-6%
4	6%	6%
5	11%	11%

Mean Return is calculated using the formula:

Mean Return = E[R] = (R₁+R₂+R₃+R₄+R₅)/n

Mean Return for Cherry = E[R_C] = (16%+11%+(-1%)+6%+11%)/5 = 8.6%

Mean Return for Straw = E[R_s] = (16%+23%+(-6%)+6%+11%)/5 = 10%

Sample vaiance formula

The data that is given is a sample as it only contains 5 data sets and it is not a population. So, we will use the formula for variance calculation of a sample.

Variance of a sample (with sample size n) is calculated using the formula:

σ² = [(R₁-E[R])²+(R₂-E[R])²+(R₃-E[R])²+(R₄-E[R])²+(R₅-E[R])²]/(n-1)

Here, sample size = n = 5

so, n-1 = 4

σ² = [(R₁-E[R])²+(R₂-E[R])²+(R₃-E[R])²+(R₄-E[R])²+(R₅-E[R])²]/4

For Cherry

Variance of Cherry = σ_C² = [(16%-8.6%)²+(11%-8.6%)²+(-1%-8.6%)²+(6%-8.6%)²+(11%-8.6%)²]/4 = 0.01652/4 = 0.00413

Standadrd deviation is square-root of variance

Standard deviation of Cherry = σ_C = 0.00413^1/2 = 6.42650760522385% ~ 6.43%

For Straw

Mean Return for Straw = E[R_s] = 10%

Variance of Straw = σ_s² = [(16%-10%)²+(23%-10%)²+(-6%-10%)²+(6%-10%)²+(11%-10%)²]/4 = 0.0478/4 = 0.01195

Standard deviation of Straw = σ_S = 0.01195^1/2 = 0.109316055545377 = 10.9316055545377% ~ 10.93%

Answer

	Cherry		Straw
Variance	0.00413		0.01195
Standard deviation	6.43	%	10.93	%