Box Plots

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Box Plots


Purpose

To graphically compare the data from a process at different levels, or states, of the process. Box plots display the main features of a batch of data, and permit simple comparisons of several batches. They can display, in an easy to understand graphical form, the Median, the First and Third Quartiles of the data sample, the Range, and any outliers.


Anatomy

Box Plots

Reference:Basic Statistics: Tools for Continuous Improvement

Terminology

A. Process variable being studied
B. Process number, or other form of indicator which differentiates one sub-group of data from another
C. First Quartile (Q1)– The upper edge of the Box represents the First Quartile, the observation (data point) which is located at position (n+1)/4 in the sorted data
D. Third Quartile (Q3)– The lower edge of the Box represents the Third Quartile, the observation (data point) which is located at 3(n+1)/4 in the sorted data
E. Whiskers, whose upper and lower extremes are marked by the limits:
Lower Limit = Q1-1.5(Q3-Q1) Upper Limit = Q3+1.5(Q3-Q1)
F. Median of the individual sub-group
G. Outliers

Application Cookbook

  1. Gather data and divide into sub-groups, if applicable.
  2. For each sub-group, determine number of data points.
  3. For each sub-group, calculate the First and Third Quartile values.
  4. For each sub-group, calculate the Median value.
  5. For each sub-group, calculate the upper and lower values of the whiskers.
  6. Draw the plots for each sub-group.

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