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

The variances for Cherry Jalopies, Inc., and Straw Construction Company are calculated as 0.002368 and 0.008300, respectively, while the standard deviations are computed as 4.87% for Cherry Jalopies, Inc. and 9.11% for Straw Construction Company.

Step-by-step explanation:

The student in question is seeking to calculate the variances and standard deviations for Cherry Jalopies, Inc., and Straw Construction Company's stock returns over five years. To calculate the variance, we first compute the average return for each company and then find the differences between each year's return and the average, square those differences, sum them, and then divide by the number of data points minus one. To find the standard deviation, we take the square root of the variance.

For Cherry Jalopies, Inc.:

1. Calculate the average return: (16% + 11% - 1% + 6% + 11%) / 5 = 8.6%
2. Calculate each year's deviation from the average, square it, and sum: ((16-8.6)^2 + (11-8.6)^2 + (-1-8.6)^2 + (6-8.6)^2 + (11-8.6)^2) / 4
3. Compute the variance: = 0.002368
4. Compute the standard deviation by taking the square root of the variance: = 4.87%

For Straw Construction Company:

1. Calculate the average return: (16% + 23% - 6% + 6% + 11%) / 5 = 10%
2. Calculate each year's deviation from the average, square it, and sum: ((16-10)^2 + (23-10)^2 + (-6-10)^2 + (6-10)^2 + (11-10)^2) / 4
3. Compute the variance: = 0.008300
4. Compute the standard deviation by taking the square root of the variance: = 9.11%

Answer 2

Cherry:

S = 0.01652

standard deviation = 0.128530152

Straw:

S =0.0478

And the standard deviation = 0.218632111

Step-by-step 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