The Approximate Percentile function, composed of ApproxPercentileReduce and ApproxPercentileMap, computes approximate percentiles for one or more columns of data. The nth percentile is the smallest value in a data set that is greater than n% of the values. The larger the data set, the more accurate the approximate percentile.
The Approximate Percentile function is based on an algorithm developed by Greenwald and Khanna. The function gives e-approximate quantile summaries of a set of N elements, where e is the error (the desired accuracy of the approximation). Given any rank r, an e-approximate summary returns a value whose rank r' is in the interval [r - eN, r + eN]. The algorithm has a worst-case space requirement of O((1/e) * log(eN)).
When running the Approximate Percentile function, you specify e with the ErrorRate parameter.