Quantile

  A random variable X is described by a distribution function F(x) and also, if F(x) is differentiable, by a probability density function . The quantile (or fractile ) x_q of the distribution, with 0 < q <1, is defined by

i.e. q is the probability of observing X < x_q. The quantile x_1/2 is called the median of the distribution; x_1/4 and x_3/4 are the lower and upper quartiles. In analogy, also quintiles and percentiles, etc., are in use.