Box Plots

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Box Plots

• Very useful graphical descriptive statistic
• Gives a clear picture of the data without using
  parametric statistics (such as the mean and
  standard deviation)
• Can tell if the data is skewed
• Outliers are obvious
• Easy to compare data by time period, location, or
  other variables of interest

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Information Needed

• Data Array
• Minimum values
• Maximum values
• 25th percentile q1
• 50th percentile q2 median
• 75th percentile q3

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Box Plot (a.k.a. Box-Whisker Plot)
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Box Construction q1 q3
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Non-parametric View of the Data
Min
Max
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Interquartile Range (H) q3 q1
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Fences are calculated based on the
interquartile range. (They are not included in
the plot).
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Whisker Construction
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Outliers are beyond the fences
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Final Box Plot (does not include fences)
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Variations

• All outliers look the same (no extreme outliers)
• Whiskers go to maximum and minimum values (no
  recognition of outliers)
• Mean shown as a plus sign
• Quartiles designated as q1, q2 q3
• Values shown on the plot
• Boxes can be shown horizontally or vertically,
  depending on aesthetics

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Example of side-by-side Box Plots