A random sample of 20 patients on the length of stay (in days) in​ short-term hospitals is shown below.

2	3	4	5	5
8	8	13	13	13
15	17	19	21	21
21	25	25	47	55
Sketch a modified boxplot.

Be sure to give your graph a title and label the axis.

Once complete, scan or take a picture and upload it here.

To sketch a modified boxplot for the data provided, follow these steps:

### Data:
2, 3, 4, 5, 5, 8, 8, 13, 13, 13, 15, 17, 19, 21, 21, 21, 25, 25, 47, 55

### Steps for Modified Boxplot:

1. **Order the Data**: The data is already ordered.
2. **Identify the Five-Number Summary**:
   - Minimum: \(2\)
   - First Quartile \(Q_1\) (25th percentile): The median of the lower half of the data = \(8\)
   - Median \(Q_2\) (50th percentile): Middle of the dataset = \(15\)
   - Third Quartile \(Q_3\) (75th percentile): The median of the upper half of the data = \(25\)
   - Maximum: \(55\)

3. **Identify Outliers**:
   - **Interquartile Range (IQR)**: \(Q_3 - Q_1 = 25 - 8 = 17\)
   - **Outlier Thresholds**:
     - Lower threshold: \(Q_1 - 1.5 \times IQR = 8 - 1.5(17) = -17.5\) (No lower outliers since all values are above 0)
     - Upper threshold: \(Q_3 + 1.5 \times IQR = 25 + 1.5(17) = 50.5\)
   - Any data points greater than \(50.5\) will be considered outliers. In this case, \(55\) is an outlier.

4. **Boxplot Construction**:
   - Draw a number line that covers the range of your data (e.g., 0 to 60).
   - Draw a box from \(Q_1 = 8\) to \(Q_3 = 25\).
   - Draw a line at the median \(Q_2 = 15\).
   - Draw "whiskers" from \(Q_1 = 8\) to the smallest non-outlier \(2\), and from \(Q_3 = 25\) to the largest non-outlier \(47\).
   - Plot \(55\) as a single point beyond the upper whisker, marking it as an outlier.

5. **Label the Axes**:
   - X-axis: Label as "Length of Stay (in days)".
   - Title: "Modified Boxplot of Length of Stay for 20 Patients".

### Next Step:
Please sketch this boxplot based on the steps outlined and upload the image for review. 

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### Would you like any further details or clarifications? Here are 5 relative questions to expand on this:

1. How do you interpret outliers in a modified boxplot?
2. What are some common applications of boxplots in healthcare statistics?
3. Can you calculate the mean length of stay from the dataset provided?
4. How does a modified boxplot differ from a standard boxplot?
5. What is the impact of skewed data on the shape of a boxplot?

**Tip:** Always double-check if your dataset contains outliers, as they can significantly affect interpretations of your results!

A random sample of 20 patients on the length of stay (in days) in​ short-term hospitals is shown below.

2 3 4 5 5 8 8 13 13 13 15 17 19 21 21 21 25 25 47 55

Sketch a modified boxplot.

Be sure to give your graph a title and label the axis.

Once complete, scan or take a picture and upload it here.

Learn how to create a modified boxplot for a sample of 20 patients based on their length of stay in short-term hospitals. The dataset includes key statistics such as the five-number summary and identifies outliers using the interquartile range (IQR). Suitable for students in Grades 10-12.

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