To find the five-number summary (lowest value, first quartile, median, third quartile, and highest value) for the data set, we need to:

1. Sort the data in ascending order.
2. Identify the lowest and highest values.
3. Determine the median.
4. Find the first quartile (Q1) and third quartile (Q3).

Step 1: Sort the Data

Sorted dataTo find the five-number summary (lowest value, first quartile, median, third quartile, and highest value) for the data set, we need to:

1. Sort the data in ascending order.
2. Identify the lowest and highest values.
3. Determine the median.
4. Find the first quartile (Q1) and third quartile (Q3).

Step 1: Sort the Data

Sorted
6, 8, 9, 10, 10, 10, 12, 14, 14, 16, 16, 16, 17, 18, 20, 20, 20, 22, 22, 25

Step 2: Identify the Lowest and Highest Values

• Lowest value (Min): 6
• Highest value (Max): 25

Step 3: Determine the Median

The median is the middle value of the sorted data. Since there are 20 data points, the median is the average of the 10th and 11th values.

• Median: $\frac{16 + 16}{2} = 16$

Step 4: Find the First Quartile (Q1) and Third Quartile (Q3)

• First Quartile (Q1): The median of the first half of the data (before the overall median). This is the 5th and 6th data points' average.

  • Q1: $\frac{10 + 10}{2} = 10$

• Third Quartile (Q3): The median of the second half of the data (after the overall median). This is the 15th and 16th data points' average.

  • Q3: $\frac{20 + 20}{2} = 20$

The Five-Number Summary:

• Lowest Value: 6
• First Quartile (Q1): 10
• Median: 16
• Third Quartile (Q3): 20
• Highest Value: 25

Would you like details or have any questions?

Here are some related questions you might find helpful:

1. How do you calculate the interquartile range (IQR) from a five-number summary?
2. What does the median tell you about a data set?
3. How can outliers be identified using a box plot?
4. What is the significance of the first and third quartiles in data analysis?
5. How does the five-number summary help in understanding the spread of data?
6. Can a box plot show more than just the five-number summary?
7. How do you interpret a box plot when comparing two data sets?
8. How does the five-number summary differ from the mean and standard deviation?

Tip: When interpreting data distributions, the five-number summary provides a quick snapshot of the data's central tendency, variability, and potential outliers.