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To determine whether there are outliers in the given data set using the 1.5 × IQR rule, we need to follow these steps:

1. **List of data**: The data set given is:  
   \( 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58 \).

2. **Calculate the Quartiles**:  
   First, let's find the first quartile (Q1) and the third quartile (Q3).
   - The data set is already sorted.
   - \( Q1 \) (the first quartile) is the 25th percentile, which for this data set is the median of the lower half:  
     \( 9, 17, 20, 21, 27 \). The median is \( Q1 = 20 \).
   - \( Q3 \) (the third quartile) is the 75th percentile, which is the median of the upper half:  
     \( 30, 31, 32, 35, 58 \). The median is \( Q3 = 32 \).

3. **Interquartile Range (IQR)**:  
   \( IQR = Q3 - Q1 = 32 - 20 = 12 \).

4. **Calculate the outlier boundaries**:  
   Using the 1.5 × IQR rule, the boundaries for outliers are:
   - Lower bound: \( Q1 - 1.5 \times IQR = 20 - 1.5 \times 12 = 20 - 18 = 2 \).
   - Upper bound: \( Q3 + 1.5 \times IQR = 32 + 1.5 \times 12 = 32 + 18 = 50 \).

   Any data point outside these bounds (less than 2 or greater than 50) will be considered an outlier.

5. **Check for outliers**:  
   - The data point 9 is **not** an outlier since it is greater than the lower bound of 2.
   - The data point 58 is **an outlier** because it is greater than the upper bound of 50.

Therefore, based on the 1.5 × IQR rule, **there is only one outlier at 58 minutes**. This matches answer choice **C**.

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Would you like further details on any part of the process, or do you have any additional questions?

Here are five related questions to consider:
1. How do you calculate quartiles in a larger data set?
2. What is the purpose of the IQR rule in detecting outliers?
3. How does the IQR compare to other methods of outlier detection like the Z-score?
4. Could there be a situation where using the IQR rule is not appropriate?
5. How do extreme outliers affect statistical analysis?

**Tip**: Always ensure your data is sorted before calculating quartiles, as this affects the accuracy of your results.

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list: 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58. One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5 × IQR rule for outliers, is there evidence to support the student’s claim?

Learn how to identify outliers using the 1.5 × IQR rule in a data set of puzzle completion times for 11 students. This guide walks through the process of calculating quartiles, IQR, and determining the boundaries for outliers. Suitable for students in Grades 8-10.

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