Question

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.
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.)

Answer 1

Answer:

Cherry:

S = 0.01652

standard deviation = 0.128530152

Straw:

S =0.0478

And the standard deviation = 0.218632111

Explanation:

Cherry Jalopies:

variance:

∑ (n1 - median)2

First we calcualte the median:

(0.16 + 0.11 - 0.01 + 0.06 + 0.11)/5 = 0.086

Then we calculate the variance:

which is each the sum of return minus the median squared

$(0.16-0.086)^{2} +(0.11-0.086)^{2} +(-0.01-0.086)^{2} +(0.06-0.086)^{2} +(0.11-0.086)^{2}$

S = 0.01652

standard deviation: √S = √0.01652 = 0.128530152

Straw

we do the same procedure:

(0.16+0.23 -0.06+0.06+0.11)/5 = 0.1

Then we do the variance:

0.0478

And the standard deviation:√S = √0.0478 = 0.218632111