The image shows a statistics problem involving the five-number summary of a dataset. Let’s walk through the steps needed to determine the outlier bounds.

Five-number summary:

• Minimum (Q0): 46
• First Quartile (Q1): 56
• Median (Q2): 61
• Third Quartile (Q3): 67
• Maximum (Q4): 70

Step 1: Interquartile Range (IQR)

The IQR measures the spread of the middle 50% of the dataThe image shows a statistics problem involving the five-number summary of a dataset. Let’s walk through the steps needed to determine the outlier bounds.

Five-number summary:

• Minimum (Q0): 46
• First Quartile (Q1): 56
• Median (Q2): 61
• Third Quartile (Q3): 67
• Maximum (Q4): 70

Step 1: Interquartile Range (IQR)

The IQR measures the spread of the middle 50% of the
$\text{IQR} = Q3 - Q1 = 67 - 56 = 11$

Step 2: Outlier Boundaries

• Lower Bound:
  $\text{Lower Bound} = Q1 - 1.5 \times \text{IQR} = 56 - 1.5 \times 11 = 56 - 16.5 = 39.5$ Any value below 39.5 will be considered a lower outlier.

• Upper Bound:
  $\text{Upper Bound} = Q3 + 1.5 \times \text{IQR} = 67 + 1.5 \times 11 = 67 + 16.5 = 83.5$ Any value above 83.5 will be considered an upper outlier.

Answers:

• An observation is considered an outlier if it is below: 39.5
• An observation is considered an outlier if it is above: 83.5

Would you like further clarification or more examples?

5 Related Questions:

1. What is the purpose of the IQR in detecting outliers?
2. How is the five-number summary used to describe the spread of data?
3. What happens if a dataset contains no outliers?
4. How do we adjust if extreme outliers are detected beyond 3 IQRs?
5. Can box plots visually represent outliers?

Tip: For large datasets, plotting the data using a box plot can provide a quick visualization of outliers and the five-number summary.