A common first step in an analysis of a data set is
to sort the values. Given a data set x1, x2, . . . ,xn, we may sort the values to obtain an increasing sequence x(1) ≤ x(2) ≤ x(3)… ≤ x(n). This is called the order statistics which gives an indication of the shape of the distribution so to have an idea about where the data is concentrated and where they are sparce.
The sample quantiles are related to the order statistics. Unfortunately, there is not a universally accepted definition of them. the most popular sample quantile is ˜q0:50, also known as the sample median, x͂. The closest runners-up are the first quartile ˜q0:25 and the third quartile ˜q0:75 (the second quartile is the median).
> quantile(mtcars$mpg, c(0.25))
> quantile(mtcars$mpg, c(0.75))
> quantile(mtcars$mpg, c(0.25, 0.75))