Features of box plots

A box plot is based on the five-number summary for the data set:

  • the minimum value
  • the first (or lower) quartile
  • the median
  • the third (or upper) quartile and
  • the maximum.

Generally a box plot appears without the data.

Box plot of arm span showing rectangle in centre with horizontal lines at either end. The rectangle (or box) covers the lower quartile, median and upper quartile. The lines (or whiskers) stretch to the maximum and minimum.

Illustration of the components of a box (and whisker) plot.

 

Using a stacked dot plot at the same time as the box plot can help students visualise the data distribution.

Sixty stacked data values under a box plot showing the data distribution.

A box plot and the data it represents.

 

The software TinkerPlots can show the percentage of the data in each part of the box plot.

Same plot represented above with each quarter of the data highlighted.

Box plot highlighting each quarter of the data set.

 

The next step is using box plots to make informal inferences.

The amount of overlap of box plots for two data sets helps determine whether a difference in the data sets (and their underlying populations) is meaningful or not.

Criteria are discussed in the article Box Plots in the Australian Curriculum on the AAMT website.


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Curriculum links

Year 10: Construct and interpret box plots and use them to compare data sets

ACMSP249

Source

Australian Curriculum, Assessment and Reporting Authority (ACARA)