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To identify the outliers in the data set of travel times, we can use the interquartile range (IQR) method. First, let's order the data points and calculate the quartiles:

Data: \( \{5, 10, 10, 10, 12, 15, 20, 20, 25, 30, 30, 40, 40, 50, 60\} \)

### Steps:
1. **Find the Quartiles**:
   - **Q1 (25th percentile)**: Middle value between the 4th and 5th values in the ordered list.
   - **Q3 (75th percentile)**: Middle value between the 11th and 12th values in the ordered list.

2. **Calculate the IQR**:
   - **IQR**: \( Q3 - Q1 \)

3. **Identify Outliers**:
   - **Lower Boundary**: \( Q1 - 1.5 \times \text{IQR} \)
   - **Upper Boundary**: \( Q3 + 1.5 \times \text{IQR} \)

Let's calculate these values to determine the boundaries for low and high outliers, and then identify which of the travel times fall outside these boundaries.The calculations yield the following results:
- **First Quartile (Q1)**: 11 minutes
- **Third Quartile (Q3)**: 35 minutes
- **Interquartile Range (IQR)**: 24 minutes
- **Lower Boundary for Outliers**: -25 minutes (no practical impact since travel time cannot be negative)
- **Upper Boundary for Outliers**: 71 minutes

Given these boundaries, we can determine that there are no outliers in your data set because all travel times are between 5 and 60 minutes, which falls within the calculated bounds.

Do you need further details or have any other questions on this analysis?

**Related questions you might consider:**
1. How would the outliers change if we used a different multiplier other than 1.5 for the IQR method?
2. What impact does the range of data (e.g., maximum and minimum values) have on the presence of outliers?
3. How do outliers influence the mean and median of the dataset?
4. Would any travel times become outliers if more data points were added above 60 minutes?
5. How do outlier detection methods differ between different fields, such as statistics versus data science?

**Tip**: When assessing data for outliers, always consider the context and scale of measurements as these can influence whether unusual values truly deviate from expected patterns.

Here are the travel times in minutes for 15 workers in North Carolina, chosen at random by the Census Bureau. Identify the boundaries for outliers. Determine which of the values are outliers, if any.

Analyze travel times for 15 workers in North Carolina and identify outliers using the Interquartile Range (IQR) method. Learn how to calculate quartiles, determine IQR, and set boundaries for outliers. Suitable for high school students.

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