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Let's begin by finding the five-number summary for the given data set:

### Data:
3, 8, 8, 5, 2, 9, 8, 7, 9, 6, 9, 4, 1, 6, 2, 9, 8, 7, 7, 9

First, we will sort the data in ascending order:

1, 2, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9

Now, we can calculate the five-number summary:

1. **Minimum (Min)**: The smallest value in the data set.
   \[
   \text{Min} = 1
   \]

2. **First Quartile (Q1)**: The median of the lower half of the data (excluding the median if the number of data points is odd).
   The lower half of the data is:
   \[
   1, 2, 2, 3, 4, 5, 6, 6, 7, 7
   \]
   The median of this half (Q1) is:
   \[
   Q1 = \frac{5 + 6}{2} = 5.5
   \]

3. **Median (Q2)**: The middle value of the entire data set.
   The median of the full data set is:
   \[
   \text{Median (Q2)} = 7
   \]

4. **Third Quartile (Q3)**: The median of the upper half of the data.
   The upper half of the data is:
   \[
   7, 8, 8, 8, 8, 9, 9, 9, 9, 9
   \]
   The median of this half (Q3) is:
   \[
   Q3 = \frac{8 + 8}{2} = 8
   \]

5. **Maximum (Max)**: The largest value in the data set.
   \[
   \text{Max} = 9
   \]

### The five-number summary is:
- Min = 1
- Q1 = 5.5
- Median (Q2) = 7
- Q3 = 8
- Max = 9

### Box-and-Whisker Plot:
Based on this summary, you can now choose the correct box-and-whisker plot. From the choices (A or B), I would need more context to determine which one is correct based on their labels. However, you can check which one shows:
- The minimum at 1,
- The lower quartile at 5.5,
- The median at 7,
- The upper quartile at 8,
- And the maximum at 9.

Let me know if you want further details or if you have any questions.

### Here are five related questions to expand on this topic:
1. How do you calculate interquartile range (IQR) using the five-number summary?
2. What does the box in the box-and-whisker plot represent?
3. How do outliers affect the box-and-whisker plot?
4. What are the advantages of using a box-and-whisker plot for data representation?
5. How do you interpret the spread of data from a box-and-whisker plot?

### Tip:
When calculating the quartiles, always ensure the data is sorted in ascending order before determining the median and quartiles.

Find the five-number summary for the given data set: 3, 8, 8, 5, 2, 9, 8, 7, 9, 6, 9, 4, 1, 6, 2, 9, 8, 7, 7, 9. Draw a box-and-whisker plot and choose the correct plot (A or B).

Learn how to calculate the five-number summary for the data set: 3, 8, 8, 5, 2, 9, 8, 7, 9, 6, 9, 4, 1, 6, 2, 9, 8, 7, 7, 9. Understand quartiles and draw a box-and-whisker plot with the correct plot chosen based on minimum, quartiles, median, and maximum.

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