Five-number summary:

1. Minimum: The smallest value in the dataset is 9.

2. Lower quartile (Q1): The lower quartile is the median of the lower half of the data (excluding the overall median). The lower half of the data set is: $9, 10, 12, 18, 20, 20$ The median of this subset is the average of the 3rd and 4th values: $Q1 = \frac{12 + 18}{2} = 15$

3. Median (Q2): The median of the entire dataset is the middle value(s). Since we have 12 numbers, the median is the average of the 6th and 7th values: $Q2 = \frac{20 + 27}{2} = 23.5$

4. Upper quartile (Q3): The upper quartile is the median of the upper half of the data (excluding the overall median). The upper half of the dataset is: $27, 28, 29, 29, 35, 36$ The median of this subset is the average of the 3rd and 4th values: $Q3 = \frac{29 + 29}{2} = 29$

5. Maximum: The largest value in the dataset is 36.

Interquartile Range (IQR):

The interquartile range is the difference between the upper quartile (Q3) and the lower quartile (Q1): $IQR = Q3 - Q1 = 29 - 15 = 14$

Summary:

• Minimum: 9
• Lower quartile (Q1): 15
• Median (Q2): 23.5
• Upper quartile (Q3): 29
• Maximum: 36
• Interquartile range (IQR): 14

Would you like further explanation or more details on quartiles?

Here are 5 related questions:

1. How are quartiles used to detect outliers in a data set?
2. Can the interquartile range ever be negative?
3. What is the significance of the interquartile range in statistics?
4. How would the five-number summary change if an additional value is added to the dataset?
5. How does the five-number summary differ from measures like mean and standard deviation?

Tip: The interquartile range is a robust measure of spread, less affected by extreme values than the range or standard deviation!