[see also quantiles!]

Quartiles are scores that split a set of scores into four equal sized subsets. If you had scores: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 then the quartiles at 2.5, 5.5 and 7.5 split the distribution into four about equally sized subsets:
1 and 2
3 , 4 and 5
6 and 7
8, 9 and 10
You can see that the split isn’t perfect and the quartiles 2.5 and 7.5 (with the median at 5.5) don’t actually exist in the data so are a bit arbitrary. However, seeing where the scores are that, with the median, split your dataset of scores into four as nearly as possible equal sized subsamples is one very useful way to summarise data and helps remind us that the mean is not the only summary statistic that matters.


Here’s a histogram of a set of scores with mean 40.4 (with a theoretically possible range of scores from zero to 100). The quartiles here are at 36.9 and 43.8, very tight around that mean.

And here’s another similar sized set of scores with very similar mean (44.7) but very different scatter about that mean, and hence very different quartiles: 32.5 and 50.2.

Try also #

Standard deviation
Summary statistics

Chapters #

Chapter 5

Other resources for more detail (not all ready yet) #

Rblog post about the ECDF (with lots on quantiles)
Rblog post about confidence intervals around quantiles
Rblog post about mapping individual scores to where they come in large sample distributions of scores
Entries in Rblog post containing code that made the plots here:
illustrating quartiles and the IQR
more on quartiles

Online applications #

Shiny app to compute the quartiles for a set of data and plot the ECDF for the distribution with confidence intervals around quartiles or any quantiles you want.
Shiny app to compute quartiles and other summary statistics for a set of data and plot the histogram for the distribution (in preparation!)

Dates #

Created 1.xi.21, last updated 19.viii.23.

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