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Let's break down the problem in the image you provided step by step. The question asks for two things:

### a) Calculate the average return on capital for each company over the given period (2002–2008).
We will calculate the arithmetic mean for both companies A and B using the provided data.

The formula for the average return on capital is:

\[
\text{Average} = \frac{\sum \text{Return}}{n}
\]

Where:
- \(\sum \text{Return}\) is the sum of the returns over the years.
- \(n\) is the number of years (in this case, 7 years from 2002 to 2008).

### b) Calculate the absolute average deviation, variance, standard deviation, and coefficient of variation for each company.

For this, we use the following formulas:

1. **Absolute Average Deviation:**
   \[
   \text{Absolute Average Deviation} = \frac{\sum |\text{Return} - \text{Average}|}{n}
   \]

2. **Variance:**
   \[
   \text{Variance} = \frac{\sum (\text{Return} - \text{Average})^2}{n}
   \]

3. **Standard Deviation:**
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}}
   \]

4. **Coefficient of Variation (CV):**
   \[
   \text{CV} = \frac{\text{Standard Deviation}}{\text{Average}} \times 100
   \]

Let me calculate these for both companies using the data provided.Here are the results for each company:

### Company A:
1. **Average Return on Capital:** \( 8.16\% \)
2. **Absolute Average Deviation:** \( 17.62\% \)
3. **Variance:** \( 426.33 \)
4. **Standard Deviation:** \( 20.65\% \)
5. **Coefficient of Variation (CV):** \( 253.13\% \)

### Company B:
1. **Average Return on Capital:** \( 5.79\% \)
2. **Absolute Average Deviation:** \( 1.16\% \)
3. **Variance:** \( 1.86 \)
4. **Standard Deviation:** \( 1.36\% \)
5. **Coefficient of Variation (CV):** \( 23.54\% \)

The results indicate that **Company A** has a much higher variation and volatility in its return on capital compared to **Company B**, as shown by its higher standard deviation and coefficient of variation.

Would you like further details or clarification on any of the calculations?

Here are 5 related questions for further exploration:
1. How would these variations affect the risk assessment for each company?
2. How could the negative returns in 2005 and 2006 for Company A impact long-term growth?
3. What other financial ratios could provide deeper insight into the stability of these companies?
4. How does the coefficient of variation help compare risk between companies?
5. What strategies could Company A employ to reduce its volatility?

**Tip:** The coefficient of variation is particularly useful when comparing the relative risk of two investments, as it takes both the mean return and the standard deviation into account.

Xác định tỷ lệ lãi trên vốn của hai công ty từ năm 2002 đến năm 2008 và tính toán các thông số như độ lệch chuẩn, phương sai, hệ số biến thiên.

Calculate the average return on capital, absolute average deviation, variance, standard deviation, and coefficient of variation for two companies from 2002 to 2008. Detailed step-by-step statistical analysis for students in Grades 11-12.

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