The question asks for the five-number summary (minimum, Q1, median, Q3, and maximum) for the given dataset:

Data Set: 1, 6, 9, 15, 23, 24, 44, 66, 67, 71, 72

Steps to calculate the five-number summary:

1. Minimum: The smallest number in the dataset.

   • Min = 1

2. Maximum: The largest number in the dataset.

   • Max = 72

3. Median: The middle number when the dataset is sorted. Since there are 11 numbers, the median is the 6th number.

   • Median = 24

4. First Quartile (Q1): This is the median of the lower half of the dataset (the first 5 numbers: 1, 6, 9, 15, 23). The median of this subset is the 3rd number.

   • Q1 = 9

5. Third Quartile (Q3): This is the median of the upper half of the dataset (the last 5 numbers: 44, 66, 67, 71, 72). The median of this subset is the 3rd number.

   • Q3 = 67

Final five-number summary:

• Min = 1
• Q1 = 9
• Median = 24
• Q3 = 67
• Max = 72

Would you like more details on any of the steps or have any other questions?

Here are 5 related questions to expand your understanding:

1. How is the interquartile range (IQR) calculated from the five-number summary?
2. How would the five-number summary change if an additional data point was added?
3. What is the significance of quartiles in data distribution?
4. How does the five-number summary relate to box plots in statistics?
5. Can you calculate the range using the five-number summary?

Tip: The interquartile range (IQR) is a good measure of data spread, calculated as $\text{IQR} = Q3 - Q1$.