https://file.aiquickdraw.com/mathbot/file/17267312380486re9axj7.jpg

The five-number summary provided is:

- Minimum: 46
- First Quartile (Q1): 51
- Median: 59
- Third Quartile (Q3): 65
- Maximum: 70

To identify outliers, we can use the Interquartile Range (IQR) method. The steps are:

1. **Calculate the IQR**:  
   \[
   \text{IQR} = Q3 - Q1 = 65 - 51 = 14
   \]

2. **Determine the fences for outliers**:  
   - Lower Fence = \( Q1 - 1.5 \times \text{IQR} \)  
     \[
     \text{Lower Fence} = 51 - 1.5 \times 14 = 51 - 21 = 30
     \]
   - Upper Fence = \( Q3 + 1.5 \times \text{IQR} \)  
     \[
     \text{Upper Fence} = 65 + 1.5 \times 14 = 65 + 21 = 86
     \]

Thus, an observation is considered an outlier if it is:
- **Below** 30
- **Above** 86

Would you like more details or have any questions? Here are 5 follow-up questions:

1. How are extreme outliers classified differently from regular outliers?
2. What is the significance of the interquartile range (IQR) in data analysis?
3. Can the IQR method miss certain types of outliers in non-normal data distributions?
4. How can box plots be used to visually identify outliers in a dataset?
5. What other methods, besides the IQR rule, are used to detect outliers?

**Tip**: Outliers can have a large impact on statistical analyses, especially in small datasets, so detecting and addressing them is crucial.

The five-number summary of a dataset was found to be: 46, 51, 59, 65, 70. An observation is considered an outlier if it is below: ____, and if it is above: ____.

Learn how to identify outliers from a five-number summary using the Interquartile Range (IQR) method. In this example, the five-number summary is 46, 51, 59, 65, 70. The IQR is calculated to determine if any observations fall below or above the outlier thresholds. Suitable for students in Grades 9-12.

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