The word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x . This particular meaning has close ties to the so-called quantile function, a function which assigns to each probability p attained by a certain probability density function f = f(X) a value Q_f(p) defined by Q_f(p) = {x:Pr(X<=x) = p}. The kth n-tile P_k is that value of x, say x_k, which corresponds to a cumulative frequency of N k/n. If n = 4, the quantity is called a quartile, and if n = 100, it is called a percentile.
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