Let's first organize the data and then solve for the five-number summary and draw the box-and-whisker plot.

Step 1: Arrange the Data in Ascending Order

The data set you provided is:

4, 8, 8, 5, 2, 9, 8, 7, 9, 6, 9, 4, 2, 6, 2, 9, 8, 7, 7, 9

Arranging it in ascending order:

2, 2, 2, 4, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9

Step 2: Find the Five-Number Summary

The five-number summary consists of:

1. Minimum: The smallest value in the data set.

   • Minimum = 2

2. First Quartile (Q1): The median of the lower half of the data.

   • The lower half of the data: 2, 2, 2, 4, 4, 5, 6, 6, 7, 7
   • The median of these values is the average of the 5th and 6th values: (4 + 5) / 2 = 4.5
   • Q1 = 4.5

3. Median (Q2): The middle value of the entire data set.

   • The middle value in the ordered data set is the average of the 10th and 11th values: (7 + 7) / 2 = 7
   • Median = 7

4. Third Quartile (Q3): The median of the upper half of the data.

   • The upper half of the data: 8, 8, 8, 8, 9, 9, 9, 9, 9
   • The median of these values is the 5th value, which is 9.
   • Q3 = 9

5. Maximum: The largest value in the data set.

   • Maximum = 9

Five-Number Summary

• Minimum: 2
• Q1: 4.5
• Median (Q2): 7
• Q3: 9
• Maximum: 9

Step 3: Box-and-Whisker Plot

The box-and-whisker plot represents the five-number summary:

• A box is drawn from Q1 to Q3 with a line (the median) inside the box.
• Whiskers extend from the box to the minimum and maximum values.

I'll now create the box-and-whisker plot. matplotlib.pyplot as plt

Data points for box plot

data = [2, 2, 2, 4, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9]

Create box plot

plt.figure(figsize=(8, 6)) plt.boxplot(data, vert=False)

Title and labels

plt.title('Box-and-Whisker Plot') plt.xlabel('Data Values')

Show the plot

plt.show()Here is the box-and-whisker plot based on the given data. It visually represents the five-number summary:

• The box spans from Q1 (4.5) to Q3 (9) with a line at the median (7).
• The whiskers extend from the box to the minimum (2) and maximum (9) values.

Do you need further details on any of these calculations or the plot? Let me know!

Here are 5 related questions you might find interesting:

1. How would the box-and-whisker plot change if the data had more extreme values?
2. How do you interpret outliers in a box-and-whisker plot?
3. What does the interquartile range (IQR) represent in this context?
4. How does the median differ from the mean in a data set like this?
5. What is the significance of the whiskers and how do they help in data analysis?

Tip: The box-and-whisker plot is especially useful for identifying skewness in data. If the median is closer to Q1 or Q3, the data may be skewed.