Question

Can anyone explain the difference between a percentile / quantile / quartile ?

Answer 1

all these tiles represent a position within the data set.

percent means 1/100, divide the number of elements in the data set by 100 to determine 1percentile

quantile ... havent heard this term

quartile means 1/4, divide the number of elements in the data set by 4 to determine 1quartile

Answer 2

Let's say you have a set of test scores ranging from 0 to 100. Let's also say the average score was 50 and that the scores are normally distributed.

To say a particular score \(N\) is called the \(k\)-th percentile means to say that \(k\%\) of the total scores fall above \(N\), or equivalently, \((100-k)\%\) of the total scores fall below \(N\).

For example, if someone scores \(80\%\), that means they belong to the 20th percentile.

As @amistre64 mentioned, a quartile can be the score marking the 25th, 50th, or 75th percentile.

A quantile is the general term for a percentile. For example, tertiles can be the 33rd or 66th/67th percentiles. Deciles can be the 10th, 20th, ..., 90th percentiles.