You have received a year-end bonus of $5000. You decide to invest the money in the stock market and have narrowed your investment options down to two mutual funds. the following data represent the historical quarterly rates of return of each mutual fund for the past 20 quarters (5 years).
Mutual Fund A
1.3, -0.3, 0.6, 608, 5.0, 5.2, 4.8, 2.4, 3.0, 1.8, 7.3, 8.6, 3.4, 3.8, -1.3, 6.4, 1.9, -0.5, -2.3, 3.1
Mutual Fund B
-5.4, 6.7, 11.9, 4.3, 4.3, 3.5, 10.5, 2.9, 3.8, 5.9, -6.7, 1.4, 8.9, 0.3, -2.4, -4.7, -1.1, 3.4, 7.7, 12.9
Describe each data set. That is, determine the shape, center and spread. Which mutual fund would you invest in and why? Also calculate the CV for both sets of data."
I know the formula for the CV is (s/x̄)x100%, and i found x̄ to be 3.05 for A, and 3.41 for B. But i do not know how to get the s value. Also, i do not know what "center and spread" mean. Could someone help me please?
p.s. x̄ is "x-bar"
To find the value of "s" in the formula for the coefficient of variation (CV), you need to calculate the standard deviation (s) of each data set.
The center of a data set refers to the measure of central tendency, which helps characterize the typical or average value in the data. Common measures of center include the mean (x̄), median, and mode. The spread of a data set refers to the variability or dispersion of the data points.
To find the center and spread of the data sets, you can use the following steps:
1. Calculate the mean (x̄) of each data set:
- For Mutual Fund A, you mentioned the mean (x̄) is 3.05.
- For Mutual Fund B, you mentioned the mean (x̄) is 3.41.
2. Calculate the standard deviation (s) of each data set:
- For Mutual Fund A, use the formula: s = √((Σ(x - x̄)²) / (n - 1))
- For Mutual Fund B, use the same formula as above to calculate the standard deviation.
Now, let's calculate the standard deviation for both sets of data:
Mutual Fund A:
1.3, -0.3, 0.6, 608, 5.0, 5.2, 4.8, 2.4, 3.0, 1.8, 7.3, 8.6, 3.4, 3.8, -1.3, 6.4, 1.9, -0.5, -2.3, 3.1
Step 1: Find the mean (x̄) of the data set.
Mean (x̄) = (1.3 - 0.3 + 0.6 + 608 + 5.0 + 5.2 + 4.8 + 2.4 + 3.0 + 1.8 + 7.3 + 8.6 + 3.4 + 3.8 - 1.3 + 6.4 + 1.9 - 0.5 - 2.3 + 3.1) / 20
= 3.05 (as you had mentioned)
Step 2: Calculate the squared differences from the mean.
Subtract the mean from each data point, then square it.
For example, for the first data point, (1.3 - 3.05)² = 2.8225.
Repeat this step for all data points.
Step 3: Calculate the sum of squared differences from the mean.
Add up all the squared differences from the previous step.
Step 4: Divide the sum of squared differences by (n - 1).
n is the number of data points, which in this case is 20.
Step 5: Take the square root of the result from step 4 to find the standard deviation.
Repeat the same process for Mutual Fund B, using the provided data.
Once you have the standard deviation for both data sets, you can calculate the coefficient of variation (CV) using the formula you mentioned: (s/x̄)x100%.
After finding the CV for each data set, compare them to determine which mutual fund would be a better investment. The mutual fund with a lower CV indicates less relative risk compared to its expected return, making it a potentially more favorable choice for investment.