2.2 Interpreting box plots
Presenting data in a box plot is a way to represent the ‘shape’ of the data. We mentioned the shape of data when talking about stemplots last week; often a common classroom task is to create a box plot from a set of data that is presented in a stemplot.
One feature of changing data from being presented in a stemplot to presenting it in a boxplot is the loss of detail in the data; a boxplot gives a summary of the data set whereas a stemplot shows each individual data item.
Activity 5
Here is another boxplot representing rainfall in one of the locations from Activity 3:
Part (a) Use these summary statistics to identify which location this boxplot represents.
Multiple choice: Stornoway, Camborne, Cardiff, Armagh
Part (b) For the location represented by this box plot, what proportion of the year do you roughly estimate has more than 50mm of rain?
Reveal answer hereAnswer
Armagh Just by looking at the median value, represented by the vertical line inside the box, it should be clear to see that this box plot cannot represent Stornoway or Camborne whose medians are close to 100, or Cardiff whose median rainfall for 2023 is higher than 100mm.
Looking at the extremes and/or quartiles would also help confirm the location and it is sensible to encourage learners to use more than one data value to check graphical representations.
Looking at the boxplot, 50mm falls roughly at the lower quartile end of the box. Nearly all the box and the upper whisker lies above it so nearly 75% of the data, or three quarters of the year.
Classroom activity idea
A nice way to help learners develop their understanding of stemplots and box plots is using a card matching activity.
One set of cards has images of stemplots, and another has images of box plots. Learners need to match each of the stemplots to the appropriate box plot which represents the data given.
For additional support a third set of cards containing the 5-figure summary statistics for each set of data could be provided.
Link to activity cards to go here.