The five number summary of a dataset was found to be:

0, 4, 5, 13, 19

**An observation is considered an outlier if it is below:**

**An observation is considered an outlier if it is above:**


To determine if any observations are outliers, we use the Interquartile Range (IQR) method. Here's the step-by-step process:

### Given five-number summary:
- Minimum = 0
- Q1 (first quartile) = 4
- Median (Q2) = 5
- Q3 (third quartile) = 13
- Maximum = 19

### Step 1: Find the IQR
\[
IQR = Q3 - Q1 = 13 - 4 = 9
\]

### Step 2: Calculate the outlier boundaries
- **Lower bound**: \( Q1 - 1.5 \times IQR \)
\[
4 - 1.5 \times 9 = 4 - 13.5 = -9.5
\]
- **Upper bound**: \( Q3 + 1.5 \times IQR \)
\[
13 + 1.5 \times 9 = 13 + 13.5 = 26.5
\]

### Conclusion:
- Any observation **below** \(-9.5\) is considered an outlier.
- Any observation **above** \(26.5\) is considered an outlier.

Would you like further details or have any questions?

Here are 5 questions to extend your understanding:
1. What is the significance of the interquartile range in identifying outliers?
2. How does the IQR method compare to other outlier detection methods, such as Z-scores?
3. Can a dataset have more than one outlier, and how would this affect the summary statistics?
4. How do extreme outliers impact the five-number summary of a dataset?
5. How would the outlier boundaries change if the IQR was larger?

**Tip**: When interpreting outliers, consider their impact on the data analysis, especially if the dataset is small, as even a few outliers can significantly skew results.

The five-number summary of a dataset was found to be: 0, 4, 5, 13, 19. An observation is considered an outlier if it is below: An observation is considered an outlier if it is above:

Learn how to determine outliers using the five-number summary and interquartile range (IQR) method. This problem walks through the steps with a dataset: 0, 4, 5, 13, 19. Find out if observations are below or above outlier thresholds using key statistical formulas. Suitable for Grades 9-12.

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