Outliers and Box Plots

Overview

This lecture covers how to identify outliers using quartiles and IQR, and how to construct and interpret a box plot (box-and-whisker plot) for visualizing data spread, outliers, and skewness.

Identifying Outliers

• High outliers are values ≥ Q3 + 1.5 × IQR; in the example, this cutoff is 21.25.
• Data values above 21.25 are considered high outliers (e.g., $33.50).
• Low outliers are values ≤ Q1 − 1.5 × IQR; in the example, this cutoff is −0.75.
• No data values below −0.75 means there are no low outliers in this set.
• Outliers indicate unusually high or low values and can cause skewness in the data.

Constructing a Box Plot

• The box in a box plot spans from Q1 (left) to Q3 (right).
• A line inside the box marks the median (Q2).
• The length of the box represents the Interquartile Range (IQR), indicating the typical spread.
• "Whiskers" extend to the lowest and highest data points that are not outliers.
• Outliers are marked by special symbols (e.g., star, circle, triangle) outside the whiskers.
• The lowest whisker extends to the minimum value not classified as an outlier (e.g., 6.5).
• The highest whisker extends to the maximum value not classified as an outlier (e.g., 14.75).

Interpreting Box Plots

• Box plots visually present the spread, center (median), and outliers of the data.
• A long right whisker or distant right outlier indicates right (positive) skew.
• Box plots are most useful for non-normal or skewed data.
• For normal data, mean and standard deviation are typically used instead of quartiles.

Key Terms & Definitions

• Quartile (Q1, Q2, Q3) — Values that divide the ordered data into four equal parts.
• IQR (Interquartile Range) — Difference between Q3 and Q1; measures data spread.
• Outlier — Data value outside the range Q1 − 1.5 × IQR or Q3 + 1.5 × IQR.
• Box Plot (Box and Whisker Plot) — Graphical display showing quartiles, median, spread, and outliers.
• Skewed Right — Data distribution with a longer right tail; higher values farther from the median.

Action Items / Next Steps

• Practice creating box plots using computer software.
• Review how to calculate quartiles and IQR.
• Observe how outliers and skewness appear in box plots.