# Quartiles

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.

Details

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 #

Variance
Standard deviation
Distribution
Histogram
Summary statistics

Chapter 5

#### Online applications #

In due course I hope to create a shiny app to compute the quartiles and other summary statistics for a set of data and plot the histogram for the distribution.

Created 1.xi.21