various software packages. All methods compute , the estimate for the -quantile (the -th -quantile, where ) from a sample of size by computing a real valued index . When is an integer, the -th smallest of the values, , is the quantile estimate. Otherwise a rounding or interpolation scheme is used to compute the quantile estimate from , , and . (For notation, see floor and ceiling functions).

The first three are piecewise constant, changing abruptly at each data point, while the