Let's work through each part of the problem shown in the image:

A. Calculate the mean, median, and mode for the data in the plot.

We need to first extract the data from the stem-and-leaf plot. Here's the dataLet's work through each part of the problem shown in the image:

A. Calculate the mean, median, and mode for the data in the plot.

We need to first extract the data from the stem-and-leaf plot. Here's the

• First row: $0, 5, 7, 9$
• Second row: $1, 2, 4, 6, 7$
• Third row: $3, 1, 2, 5, 9$

So, the complete dataset is: $0, 1, 1, 2, 2, 2, 3, 4, 5, 5, 6, 7, 7, 9, 9$

1. Mean:

The mean is the sum of the data divided by the number of values. $\text{Mean} = \frac{0 + 1 + 1 + 2 + 2 + 2 + 3 + 4 + 5 + 5 + 6 + 7 + 7 + 9 + 9}{15}$ Let's calculate the mean.

2. Median:

The median is the middle value of the dataset. Since there are 15 numbers, the 8th number is the median. The sorted dataset is: $0, 1, 1, 2, 2, 2, 3, 4, 5, 5, 6, 7, 7, 9, 9$ The 8th value is $4$, so the median is $4$.

3. Mode:

The mode is the number that appears most frequently. In this dataset, the number $2$ appears three times, making it the mode.

B. Create a box-and-whisker plot to represent the stem-and-leaf plot.

To create the box-and-whisker plot, we need the five-number summary:

1. Minimum: The smallest value is $0$.
2. First Quartile (Q1): This is the median of the first half of the data. The first half of the dataset (before the median $4$) is: $0, 1, 1, 2, 2, 2, 3$ The median of this subset is $2$, so $Q1 = 2$.
3. Median (Q2): The median is $4$ (as calculated earlier).
4. Third Quartile (Q3): This is the median of the second half of the data. The second half of the dataset (after the median $4$) is: $5, 5, 6, 7, 7, 9, 9$ The median of this subset is $7$, so $Q3 = 7$.
5. Maximum: The largest value is $9$.

Now, we have the five-number summary:

• Minimum = 0
• Q1 = 2
• Median (Q2) = 4
• Q3 = 7
• Maximum = 9

C. Find the Interquartile Range (IQR).

The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1): $IQR = Q3 - Q1 = 7 - 2 = 5$

Summary of Results:

• Mean: To be calculated.
• Median: 4
• Mode: 2
• Five-number summary:
  • Minimum = 0
  • Q1 = 2
  • Median = 4
  • Q3 = 7
  • Maximum = 9
• Interquartile Range (IQR): 5

Let me calculate the mean next.The mean of the data is $4.2$.

Final Summary:

• Mean: 4.2
• Median: 4
• Mode: 2
• Five-number summary:
  • Minimum = 0
  • Q1 = 2
  • Median = 4
  • Q3 = 7
  • Maximum = 9
• Interquartile Range (IQR): 5

Would you like more details on any part, or assistance with creating a detailed box-and-whisker plot?

Here are five related questions:

1. What are the steps for creating a stem-and-leaf plot?
2. How do we interpret a box-and-whisker plot?
3. Can a dataset have more than one mode?
4. How do quartiles divide a dataset?
5. What are other measures of spread besides the interquartile range?

Tip: When analyzing data, always check for outliers, which are values significantly different from others. These can be identified using the IQR.