To find the lower quartile (Q1) and upper quartile (Q3), we need to first order the data and then determine the 25th percentile (Q1) and the 75th percentile (Q3).

Step 1: Sort the data in ascending order

0, 1, 2, 3, 5, 6, 6, 7, 9, 9, 10, 10, 12, 13, 13, 13, 13, 13, 15, 17, 19, 20, 21, 22, 22, 22, 22, 24, 24, 25, 25, 25, 33, 35, 35, 35, 35, 38, 39, 44, 50, 56, 59, 63

There are 42 data points in total.

Step 2: Find Q1 (Lower Quartile)

• Q1 is the value at the 25th percentile, which corresponds to the 0.25 × 42 = 10.5th value. We average the 10th and 11th values.
  • 10th value: 9
  • 11th value: 10
  • $Q1 = \frac{9 + 10}{2} = 9.5$

Step 3: Find Q3 (Upper Quartile)

• Q3 is the value at the 75th percentile, which corresponds to the 0.75 × 42 = 31.5th value. We average the 31st and 32nd values.
  • 31st value: 25
  • 32nd value: 33
  • $Q3 = \frac{25 + 33}{2} = 29$

Final Quartiles:

• Lower quartile (Q1): 9.5
• Upper quartile (Q3): 29

Would you like more details or have any further questions?
Here are some additional questions to consider:

1. What is the interquartile range (IQR) of this dataset?
2. How would you calculate the median (Q2) for this dataset?
3. How does one identify outliers using quartiles?
4. Can the quartiles change if the dataset is altered by removing extreme values?
5. What is the role of quartiles in descriptive statistics?

Tip: When calculating quartiles, sorting the data first is crucial for accurate results.