Finding percentiles
From any value, x, it is fairly easy to calculate the proportion of values in a data set that are x or lower — that is, the cumulative distribution function at x.
It is also possible to do the inverse operation. Given any proportion, p, between 0 and 1, we can find a value x such that approximately this proportion, p, of values is x or lower in our data set. This is called the p'th quantile in the data set. When p is given as a percentage, the same value is called the p'th percentile.
The p'th percentile is the value x such that p percent of the data set are x or lower.
Percentiles can be read from a graph of the cumulative distribution function — they are the x-values for which the height is p percent.
Annual rainfall in Samaru
The diagram below again shows the cumulative distribution function for the annual rainfall in Samaru, Nigeria.
Drag the horizontal red line up or down to read off different percentiles from the cumulative distribution function. Observe that:
Details (optional)
The following two points are mentioned for completeness but are not needed to understand the concept of percentiles.