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Let’s break down each question step-by-step, starting with the data extraction from the table.

**1. Relative Changes in 2019-2020:**
- **Gas Price Change:**  
  - 2019 Average Gas Price: \(2.691\)  
  - 2020 Average Gas Price: \(2.258\)  
  - Relative Change = \(\frac{2.258 - 2.691}{2.691} \times 100\% = \frac{-0.433}{2.691} \times 100\% \approx -16.09\%\)  

- **Petroleum Import Price Index Change:**  
  - 2019 Index: \(236.6\)  
  - 2020 Index: \(142.6\)  
  - Relative Change = \(\frac{142.6 - 236.6}{236.6} \times 100\% = \frac{-94.0}{236.6} \times 100\% \approx -39.73\%\)

**2. Relative Changes in 2020-2021:**
- **Gas Price Change:**  
  - 2020 Average Gas Price: \(2.258\)  
  - 2021 Average Gas Price: \(3.100\)  
  - Relative Change = \(\frac{3.100 - 2.258}{2.258} \times 100\% = \frac{0.842}{2.258} \times 100\% \approx 37.29\%\)

- **Petroleum Import Price Index Change:**  
  - 2020 Index: \(142.6\)  
  - 2021 Index: \(267.6\)  
  - Relative Change = \(\frac{267.6 - 142.6}{142.6} \times 100\% = \frac{125.0}{142.6} \times 100\% \approx 87.67\%\)

**3. Overall Relative Changes from 2012 to 2022:**
- **Gas Price Change:**  
  - 2012 Average Gas Price: \(3.680\)  
  - 2022 Average Gas Price: \(4.059\)  
  - Relative Change = \(\frac{4.059 - 3.680}{3.680} \times 100\% = \frac{0.379}{3.680} \times 100\% \approx 10.30\%\)

- **Petroleum Import Price Index Change:**  
  - 2012 Index: \(357.2\)  
  - 2022 Index: \(456.5\)  
  - Relative Change = \(\frac{456.5 - 357.2}{357.2} \times 100\% = \frac{99.3}{357.2} \times 100\% \approx 27.80\%\)

**4. Determining Volatility:**
To determine which commodity (gas or import petroleum) is more volatile, we can analyze the year-to-year changes in price:

- From the calculations above, the **Petroleum Import Price Index** has demonstrated greater percentage changes, both in the negative and positive directions, compared to the **Average Gas Price**. 
- For example:
  - In 2019-2020, the Import Price Index had a significant drop of \(-39.73\%\), whereas the Gas Price dropped by \(-16.09\%\).
  - In 2020-2021, the Import Price Index increased by \(87.67\%\), whereas the Gas Price increased by \(37.29\%\).
  
Thus, **import petroleum** appears more **volatile** than gas prices, as its values have larger fluctuations over the observed period.

Would you like more details on any of these calculations, or do you have any questions?

### Related Questions:
1. How do you determine the stability of a price index compared to an average commodity price?
2. Can volatility be quantified using a statistical measure such as standard deviation? How would that be calculated here?
3. Why might the import petroleum price index be more volatile compared to gasoline prices?
4. How do external factors like global supply chains affect the volatility of petroleum prices?
5. What methods can be used to predict future gas prices using historical data?

### Tip:
When comparing the volatility of two sets of data, look at both the range of changes and the frequency of significant fluctuations—statistical measures like standard deviation can help quantify this.

Using the table provided, calculate the relative changes in gas price and petroleum import price for the given years and determine which commodity is more volatile.

Learn how to calculate the relative changes in gas prices and petroleum import prices using the given table, and determine which commodity is more volatile. This problem involves percentage change calculations and volatility analysis, suitable for students in Grades 9-12.

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