The quantile of a distribution of values is a number xp such that a given proportion of the population values are less than or equal to xp. For example, the 0.75 quantile (also referred to as the 75th percentile or upper quartile) of a variable is a value xp such that 75% of the values of the variable fall below that value. The 0.5 quantile is the median.
numeric_exp must be a number, or a numeric expression.
Q_numeric_exp (the quantile to compute) must be a floating point number strictly between 0 and 1.
Note: If the number of data points is less than QUANTILE_ESTIMATION_THRESHHOLD, then the calculation for a median or quantile will proceed as follows:
If the data is not sorted on any columns for which calculation is requested, the data will be sorted.
The quantile position is calculated by linear interpolation.
If the number of data points is greater than or equal to QUANTILE_ESTIMATION_THRESHHOLD, then the calculation for a median or quantile will proceed as follows:
The quantile position will be estimated by the linear time selection algorithm "Randomized-Select" as described in Introduction to Algorithms by Cormen, Leiserson, and Rivest, p. 187.