Math Problem Statement
Sarah is analyzing the performance of two investment portfolios over a period of 5 years. Portfolio A has the following annual returns (in percentages): 5%, 8%, -2%, 7%, and 10%. Portfolio B has the following annual returns (in percentages): 6%, 7%, -1%, 9%, and 5%. Sarah wants to compare the two portfolios based on various statistical measures. 116. What is the mean annual return for Portfolio A? A) 5.6% B) 5.8% C) 6% D) 6.2% 117. What is the mean annual return for Portfolio B? A) 5.6% B) 5.8% C) 5.2% D) 6% 118. What is the median annual return for Portfolio A? A) 5% B) 7% C) 8% D) 10% 119. What is the range of the annual returns for Portfolio B? A) 8% B) 9% C) 10% D) 11% 120. If she added a new investment to portfolio B that returned 18%, what would the arithmetic mean? A) 12.3% B) 7.8% C) 9.1% D) 7.3%
Solution
Let's calculate the required statistical measures for both portfolios.
Step 1: Calculate the mean annual return for Portfolio A.
Portfolio A Annual Returns: 5%, 8%, -2%, 7%, 10%
The mean is calculated as:
So, the correct answer for Question 116 is: A) 5.6%
Step 2: Calculate the mean annual return for Portfolio B.
Portfolio B Annual Returns: 6%, 7%, -1%, 9%, 5%
The mean is calculated as:
So, the correct answer for Question 117 is: C) 5.2%
Step 3: Calculate the median annual return for Portfolio A.
To find the median, we first arrange the returns in ascending order:
Sorted Returns for Portfolio A: -2%, 5%, 7%, 8%, 10%
The median is the middle value:
So, the correct answer for Question 118 is: B) 7%
Step 4: Calculate the range of the annual returns for Portfolio B.
Portfolio B Annual Returns: 6%, 7%, -1%, 9%, 5%
To find the range, we first determine the minimum and maximum values:
So, the correct answer for Question 119 is: C) 10%
Step 5: Calculate the new arithmetic mean for Portfolio B with an added investment returning 18%.
Including the new return:
Updated Portfolio B Returns: 6%, 7%, -1%, 9%, 5%, 18%
The new mean is calculated as:
So, the correct answer for Question 120 is: D) 7.3%
Do you have any questions or need further clarification?
Here are some related questions:
- What is the variance of the returns for Portfolio A?
- How does the standard deviation of Portfolio B compare to Portfolio A?
- If Portfolio A had an additional year with a 15% return, what would be its new mean return?
- How would the inclusion of an outlier affect the median return in Portfolio B?
- What is the percentage difference between the mean returns of Portfolio A and Portfolio B?
Tip: When comparing portfolios, both mean return and volatility (standard deviation) are important to understand the risk and return balance.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean
Median
Range
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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