Box plots and individual value plots

What are they?

Picture of boxplotBox plots and Individual Value plots are graphs that are useful for comparing groups of data.
For example, the box plot on the right shows the results of parcel weights (in kilos) recorded at a courier company. The results have been divided into three groups that contain three different service levels (express, normal or overnight service).

The box areas represent the middle 50% of the data in each group, the middle (horizontal) lines represent the median value and the vertical lines (whiskers) represent the total range of the group.

Picture of Individual Value PlotIndividual Value plots work in a similar way, but instead of summarising the results into boxes and whiskers, the weight of each parcel is represented as a dot on the graph. So, the same data looks like this (right) when shown as an Individual Value plot.

How do you interpret Box plots and Individual Value plots?

Box plots and Individual Value plots make it easy to compare groups of data and to draw general observations.

For example, from the box plot shown, you could reasonably make the following observations:

  • It appears that parcels sent using the Normal service are generally heavier than those sent using the Express service.
  • It appears that parcels sent using the Overnight service have a larger range of weights than for other services.

Similar observations can be made from the Individual Value plot of the same data, but the Individual Value plot provides additional insight, because it clearly shows that:

  • the sample of Overnight parcels was quite small (only 10 data points)
  • just one (much heavier) parcel has caused the large range in the Overnight sample.

This example demonstrates that Individual Value plots are particularly useful when dealing with small sample sizes.

So, in summary:

  • Box plots and Individual Value plots can be used to compare groups of data, and to make general observations.
  • Care should be taken to check how much data is contained within each group, before any observations are made, particularly with Box plots.
  • If you have small sample sizes (say less than 25 data points in any one group) it is safer to use an Individual Value plot.
2019-05-10T11:25:00+00:0011th November, 2016|Categories: Article|Tags: , |