Definition:Quantile/Informal Definition

Definition
Let $S$ be a set of quantitative data.

Let $S$ be arranged in order of size.

Let $q \in \Z_{\ge 1}$ be a strictly positive integer.

Let the range of $S$ be divided into exactly $q$ class intervals such that the probability of an instance of $S$ falling into an arbitrary instance of one of these class intervals is equal to $\dfrac 1 q$.

That is, the class intervals are designed so as to have the same number of elements in them.

Then the class boundaries are known as the quantiles of $X$.