25, 50 and 75% percentiles

The 50th percentile is the median and the 25th and 75th percentiles are the lower and upper quartiles. The median and quartiles are therefore the x-values at which the height of the cumulative distribution function is 0.25, 0.50 and 0.75.

These three percentiles are therefore the positions of the central box of a box plot of the data.

Rainfall in Samaru

The diagram below shows how the median and quartiles relate to a box plot of the Samaru rainfall data.


Displaying other percentiles

A box plot is a graphical display of the minimum, maximum and the 25th, 50th and 75th percentiles that is particularly useful for comparing the distribution of values in different data sets.

In some data sets, other percentiles are more important than the 25th and 75th ones. A similar 'box' can be used to graphically display any other percentiles. It is best to alter the way the box is drawn to avoid confusion with the standard box plot.

Rainfall in Samaru

Drag the horizontal red lines to 10, 20 and 50% to display the 10th, 20th and 50th percentiles for these data.

If there is no climate change, you would expect rainfall below the 10th percentile in 1 year out of 10, and below the 20th percentile in 1 year out of 5.