In surveying error theory, once blunders and systematic errors are removed, the remaining random errors follow a normal distribution characterized by a mean and standard deviation, and probabilities of a variable falling within an interval are found by transforming to the standard normal variable Z = (X - X̄)/σ and consulting the standard normal distribution function. Outlier detection formalizes rejection of anomalous observations using deviation thresholds from the mean expressed in units of standard deviation, with the threshold itself derived from the desired cumulative probability and, more rigorously, adjusted for sample size n via a rejection probability of 1/(2n) rather than a fixed multiple of sigma. Error propagation (combination of errors) is the general law of variance propagation for a function Y = f(x1,...,xn) of several measured quantities, in which the variance of the derived quantity is the sum of the squared partial derivatives of the function with respect to each variable, each weighted by that variable's own variance.
In surveying error theory, once blunders and systematic errors are removed, the remaining random errors follow a normal distribution characterized by a mean and standard deviation, and probabilities …