To calculate the five-number summary, you need the following key statistics from the dataset:

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

Let's calculate the five-number summary for the provided dataTo calculate the five-number summary, you need the following key statistics from the dataset:

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

Let's calculate the five-number summary for the provided

Data (sorted):

0, 0, 0, 0, 0.12, 0.14, 0.16, 0.23, 0.26, 0.38, 0.41, 0.48, 0.58, 0.65, 0.67, 0.81, 0.84, 1.07, 1.26, 1.67, 2.39, 2.45, 2.5, 2.82, 2.84, 2.92, 3.1, 3.47

1. Minimum:

• 0

2. First Quartile (Q1):

• The lower half of the data has 14 values:
  0, 0, 0, 0, 0.12, 0.14, 0.16, 0.23, 0.26, 0.38, 0.41, 0.48, 0.58, 0.65
  The median of this lower half is between 0.23 and 0.26, so:
  Q1 = 0.245

3. Median (Q2):

• The median of the entire dataset (28 values) is between the 14th and 15th values (0.65 and 0.67), so:
  Median = 0.66

4. Third Quartile (Q3):

• The upper half of the data has 14 values:
  0.67, 0.81, 0.84, 1.07, 1.26, 1.67, 2.39, 2.45, 2.5, 2.82, 2.84, 2.92, 3.1, 3.47
  The median of this upper half is between 2.39 and 2.45, so:
  Q3 = 2.42

5. Maximum:

• 3.47

Five-number summary:

• Minimum = 0
• Q1 = 0.245
• Median (Q2) = 0.66
• Q3 = 2.42
• Maximum = 3.47

Would you like more details or clarification on any part of the process?

Here are five related questions you might explore:

1. How do you calculate interquartile range (IQR) from the five-number summary?
2. What does the five-number summary tell us about the distribution of the data?
3. How does one create a boxplot using the five-number summary?
4. What role does the median play in understanding skewness?
5. How do outliers affect the five-number summary?

Tip: The interquartile range (IQR) is a great way to measure the spread of the middle 50% of your data, calculated as Q3 - Q1.