Definition:Quantile/Informal Definition
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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 $X$.