Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of time to complete the 212-mile hike from Yosemite Valley across the high Sierras to the top of Mount Whitney.

Five-number summary:

Minimum: 9 days
Q1: 18 days
Median: 21 days
Q3: 28 days
Maximum: 56 days
If we use the 1.5 * IQR rule to determine whether there are any outliers, what is the right boundary?

To determine the right boundary for potential outliers using the 1.5 * IQR (Interquartile Range) rule, follow these steps:

### 1. **Calculate the Interquartile Range (IQR):**
The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

\[
\text{IQR} = Q3 - Q1 = 28\ \text{days} - 18\ \text{days} = 10\ \text{days}
\]

### 2. **Calculate the 1.5 * IQR:**
Multiply the IQR by 1.5.

\[
1.5 \times \text{IQR} = 1.5 \times 10\ \text{days} = 15\ \text{days}
\]

### 3. **Calculate the Right Boundary:**
The right boundary (upper limit) for detecting outliers is determined by adding \(1.5 \times \text{IQR}\) to Q3.

\[
\text{Right Boundary} = Q3 + (1.5 \times \text{IQR}) = 28\ \text{days} + 15\ \text{days} = 43\ \text{days}
\]

### Conclusion:
The right boundary for detecting outliers is **43 days**. Any time to complete the hike greater than 43 days would be considered an outlier according to the 1.5 * IQR rule.

Would you like more details or have any questions?

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**Related Questions:**

1. What is the left boundary for detecting outliers?
2. How many hikers took longer than the right boundary to complete the hike?
3. Can you explain the significance of each component in the five-number summary?
4. What does the median tell us about the distribution of hiking times?
5. How would the right boundary change if Q3 were 30 days instead of 28 days?

**Tip:** When analyzing data, always consider both the context and the mathematical calculations. Outliers might represent interesting cases that warrant further investigation.

Learn how to determine outliers in hiking times using the Interquartile Range (IQR) rule with a detailed example from the John Muir Trail. Analyze the five-number summary including Minimum, Q1, Median, Q3, and Maximum to find the right boundary for outliers. Suitable for high school students studying descriptive statistics.

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