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%

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:

\[
\text{Mean of Portfolio A} = \frac{5 + 8 - 2 + 7 + 10}{5} = \frac{28}{5} = 5.6\%
\]

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:

\[
\text{Mean of Portfolio B} = \frac{6 + 7 - 1 + 9 + 5}{5} = \frac{26}{5} = 5.2\%
\]

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:

\[
\text{Median of Portfolio A} = 7\%
\]

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:

\[
\text{Range of Portfolio B} = 9\% - (-1\%) = 10\%
\]

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:

\[
\text{New Mean of Portfolio B} = \frac{6 + 7 - 1 + 9 + 5 + 18}{6} = \frac{44}{6} = 7.33\%
\]

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:
1. What is the variance of the returns for Portfolio A?
2. How does the standard deviation of Portfolio B compare to Portfolio A?
3. If Portfolio A had an additional year with a 15% return, what would be its new mean return?
4. How would the inclusion of an outlier affect the median return in Portfolio B?
5. 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.

Explore the analysis of two investment portfolios over 5 years. Calculate mean annual returns for Portfolio A and Portfolio B, determine the median return for Portfolio A, and find the range of returns for Portfolio B. Understand statistical measures to assess portfolio performance.

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