Boxplot Construction and Interpretation Using StatCrunch

Describing Data with Tables and Graphs

Boxplots: Construction and Interpretation

Boxplots are graphical representations used in statistics to summarize the distribution of a dataset. They display the median, quartiles, and potential outliers, providing a visual overview of data spread and central tendency. This guide explains how to construct and interpret boxplots using StatCrunch, a statistical software tool.

• Definition: A boxplot (or box-and-whisker plot) is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

• Purpose: Boxplots help identify the central value, spread, and outliers in a dataset.

• Applications: Used in business statistics to compare distributions, detect outliers, and summarize large datasets efficiently.

Step 1: Entering Data in StatCrunch

• Open StatCrunch and locate the Data Table.

• Rename the column header for clarity (optional).

• Enter each data value in a separate row.

• Example Data: 56, 67, 68, 72, 74, 75, 88, 90, 97, 99

Step 2: Opening the Boxplot Menu

• From the top menu, click Graph.

• Select Boxplot from the dropdown menu.

Step 3: Selecting the Data Column

• In the dialog window, locate the Select column(s) area.

• Click the column name (e.g., Data) to move it to the selection box.

Step 4: Adjusting Boxplot Options (Optional)

• Use fences to identify outliers (recommended).

• Choose between Horizontal or Vertical orientation.

• Default is vertical; check the option for horizontal if desired.

• Leave other options as default unless specific display settings are needed.

Step 5: Generating the Boxplot

• Click the Compute! button.

• A new window will display the boxplot (vertical or horizontal based on selection).

Step 6: Identifying Key Features on the Boxplot

• Box: Extends from Q1 to Q3 (the interquartile range, IQR).

• Line inside box: Represents the median (Q2).

• Whiskers: Extend to the smallest and largest non-outlier values.

• Outliers: Shown as individual points beyond the whiskers.

• Hovering inside the box in StatCrunch reveals Q1, Q3, median, min, max, and IQR values.

Step 7: Modifying Display Using Options

• Click Options > Edit in the results window to adjust display settings or change the data column.

• Click Compute! again to update the boxplot.

Instructor Tip: Quartile Calculation Conventions

• StatCrunch uses its own quartile calculation convention, which may differ slightly from manual calculations or other software.

• Minor adjustments may be needed when comparing results across platforms.

Example: Boxplot with Outliers

• Data: 2, 4, 5, 6, 7, 8, 9, 10, 30

• Max value (30) is identified as an outlier.

• Hovering inside the box reveals:

  • Q1 = 5

  • Median = 7

  • Q3 = 9

  • IQR = Q3 - Q1 = 4

  • Min = 2 (Lower Limit)

  • Max = 30 (Outlier)

Boxplot Outlier Calculation

• Lower Fence: $Q_1 - 1.5 \times IQR$

• Upper Fence: $Q_3 + 1.5 \times IQR$

• Values outside these fences are considered outliers.

Additional info: StatCrunch is a widely used tool in business statistics courses for data visualization and analysis. Boxplots are essential for summarizing data distributions and identifying outliers, which are critical for business decision-making and statistical inference.