To compute the five-number summary of the data, we need to determine the following:

1. Minimum: The smallest number in the data set.
2. First Quartile (Q1): The median of the lower half of the data (25th percentile).
3. Median (Q2): The middle value of the data (50th percentile).
4. Third Quartile (Q3): The median of the upper half of the data (75th percentile).
5. Maximum: The largest number in the data set.

Step-by-Step Process:

1. Sort the Data: Arrange the data in ascending order.

Sorted Data: 0.00, 0.00, 0.00, 0.11, 0.22, 0.23, 0.31, 0.36, 0.49, 0.54, 0.65, 0.71, 0.82, 1.2, 1.23, 1.39, 1.45, 1.86, 1.98, 2.06, 2.55, 2.67, 2.75, 2.82, 2.97, 3.08, 3.21, 3.49

2. Minimum: The smallest value in the sorted data is 0.00.

3. Maximum: The largest value in the sorted data is 3.49.

4. Median (Q2): Since there are 28 numbers, the median is the average of the 14th and 15th numbers in the sorted list.

• The 14th value is 1.2.
• The 15th value is 1.23.

$\text{Median (Q2)} = \frac{1.2 + 1.23}{2} = 1.215$

5. First Quartile (Q1): The lower half of the data consists of the first 14 numbers. The median of these 14 numbers is the average of the 7th and 8th values in the sorted list.

• The 7th value is 0.31.
• The 8th value is 0.36.

$\text{First Quartile (Q1)} = \frac{0.31 + 0.36}{2} = 0.335$

6. Third Quartile (Q3): The upper half of the data consists of the last 14 numbers. The median of these 14 numbers is the average of the 7th and 8th values in this subset.

• The 7th value in the upper half is 2.55.
• The 8th value is 2.67.

$\text{Third Quartile (Q3)} = \frac{2.55 + 2.67}{2} = 2.61$

Five-Number Summary:

• Minimum: 0.00
• Q1: 0.335
• Median (Q2): 1.215
• Q3: 2.61
• Maximum: 3.49

Let me know if you'd like more details on any of these steps or have any other questions!

Here are 5 related questions for further exploration:

1. How do you calculate percentiles from data?
2. What is the interquartile range, and how is it related to the five-number summary?
3. How do you identify outliers using the five-number summary?
4. What is the significance of a skewed distribution in the context of a five-number summary?
5. How would you use the five-number summary in boxplot construction?

Tip: The five-number summary is useful for quickly identifying the spread and central tendency of a data set, and it also helps in detecting potential outliers.