https://file.aiquickdraw.com/mathbot/file/1729760429908x7nnht83.jpg

The problem in the image involves constructing a correct stem-and-leaf plot, calculating quartiles (Q1, Q2, Q3), and finding the interquartile range (IQR) for the given data set:

The recovery times (in days) for 11 individuals are:  
\[ 45, 52, 38, 60, 65, 48, 50, 48, 63, 58, 62 \]

### Steps to solve:
1. **Stem-and-leaf plot**: This type of plot organizes data based on the leading digits (stems) and trailing digits (leaves). Let's sort the data first:
\[ 38, 45, 48, 48, 50, 52, 58, 60, 62, 63, 65 \]

The stems will be the tens digits (3, 4, 5, 6), and the leaves will be the ones digits (units).

- **Stem 3**: 8
- **Stem 4**: 5, 8, 8
- **Stem 5**: 0, 2, 8
- **Stem 6**: 0, 2, 3, 5

2. **Quartiles**:
   - Q2 (median) is the middle value of the data set. Since there are 11 values, the 6th value is the median:
     \[
     Q_2 = 52
     \]
   - Q1 (lower quartile) is the median of the lower half of the data (first 5 values: 38, 45, 48, 48, 50). The middle value of this set is:
     \[
     Q_1 = 48
     \]
   - Q3 (upper quartile) is the median of the upper half of the data (last 5 values: 58, 60, 62, 63, 65). The middle value of this set is:
     \[
     Q_3 = 62
     \]

3. **Interquartile Range (IQR)**:
   \[
   IQR = Q_3 - Q_1 = 62 - 48 = 14
   \]

### Answer comparison:
Now, we compare this with the options provided:
- Option **A** has \( Q_1 = 48, Q_2 = 58, Q_3 = 62 \), and \( IQR = 14 \). The stem-and-leaf plot also matches the correct data.
- Therefore, the correct answer is **A**.

Would you like further details or explanations?

### Related Questions:
1. How do you calculate quartiles for larger datasets?
2. What are the advantages of using stem-and-leaf plots?
3. Can the IQR ever be negative, and why?
4. How do outliers affect the quartile calculation?
5. What are other common measures of variability besides IQR?

### Tip:
Always sort your data before calculating quartiles or creating stem-and-leaf plots for accuracy.

A public health department tracks the number of days it takes for 11 individuals to recover from a viral infection. The recovery times (in days) are: 45, 52, 38, 60, 65, 48, 50, 48, 63, 58, 62. Which of the following options correctly shows the stem-and-leaf plot, quartiles (Q1, Q2, Q3), and interquartile range (IQR) for the data set?

Explore how to create a stem-and-leaf plot and calculate quartiles and interquartile range (IQR) for a given data set of recovery times. This example walks through organizing data, finding quartiles (Q1, Q2, Q3), and calculating the IQR, making it an ideal resource for high school students.

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