The following data represents a sample of gas prices (cents/litre) in Toronto on 2018-08-29:
127      130      124
128      113      110
115      127      114
Find Q1, Q2, and Q3.
Calculate your answer using this Spreadsheet template.

To find the quartiles \( Q_1 \), \( Q_2 \), and \( Q_3 \), follow these steps:

1. **List the data in order**:
   The gas prices (in cents/litre) are:  
   \[
   127, 130, 124, 128, 113, 110, 115, 127, 114
   \]
   Arrange the data in ascending order:  
   \[
   110, 113, 114, 115, 124, 127, 127, 128, 130
   \]
   
2. **Find the quartiles using formulas**:
   - \( Q_1 \) is the first quartile (25th percentile).
   - \( Q_2 \) is the median (50th percentile).
   - \( Q_3 \) is the third quartile (75th percentile).

### Step-by-Step Spreadsheet Calculation:

1. **Organize the data**:  
   In a spreadsheet, input the sorted data into cells (e.g., A1:A9).

2. **Use quartile functions**:
   In most spreadsheet applications like Excel or Google Sheets:
   - For \( Q_1 \): Use `=QUARTILE(A1:A9, 1)`
   - For \( Q_2 \) (median): Use `=QUARTILE(A1:A9, 2)`
   - For \( Q_3 \): Use `=QUARTILE(A1:A9, 3)`

3. **Calculate manually for deeper understanding**:
   The positions for the quartiles are found by using:
   - \( Q_1 \) position: \( 0.25 \times (n + 1) \), where \( n \) is the number of data points.
   - \( Q_2 \) (median) position: \( 0.5 \times (n + 1) \)
   - \( Q_3 \) position: \( 0.75 \times (n + 1) \)

   For this set:
   - \( n = 9 \)
   - \( Q_1 \) position: \( 0.25 \times (9 + 1) = 2.5 \), so \( Q_1 \) is the average of the 2nd and 3rd values: \( (113 + 114) / 2 = 113.5 \)
   - \( Q_2 \) (median) position: \( 0.5 \times (9 + 1) = 5 \), so \( Q_2 = 124 \)
   - \( Q_3 \) position: \( 0.75 \times (9 + 1) = 7.5 \), so \( Q_3 \) is the average of the 7th and 8th values: \( (127 + 128) / 2 = 127.5 \)

### Final Quartiles:
- \( Q_1 = 113.5 \)
- \( Q_2 = 124 \)
- \( Q_3 = 127.5 \)

Would you like to go over any of these steps in more detail or have any questions?

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Here are 5 related questions to expand your understanding:
1. How would the quartiles change if another data point were added?
2. What is the interquartile range (IQR) for this data set?
3. How does the presence of outliers affect quartile values?
4. How are quartiles used in understanding the spread of a data set?
5. What are other common percentile-based measures in statistics?

**Tip**: When calculating quartiles manually, always sort the data first to ensure accuracy.

The following data represents a sample of gas prices (cents/litre) in Toronto on 2018-08-29: 127, 130, 124, 128, 113, 110, 115, 127, 114. Find Q1, Q2, and Q3. Calculate your answer using this Spreadsheet template.

Learn how to calculate Q1, Q2, and Q3 (quartiles) for a data set of gas prices in Toronto on 2018-08-29. This step-by-step solution uses the quartile formula and spreadsheet functions to organize and analyze the data. Suitable for students in Grades 6-8.

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