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A sample mean or sample average provides a measure of location, or central tendency, of a variable in a data set. Consider a univariate data set, which is a data set with a single variable, that consists of a random sample of n observations x₁, x₂,…, xn. The sample mean is simply the ordinary arithmetic average

For a data set y_i, i = 1, 2,…, n obtained by multiplying each xi by a constant a, i.e., yi = axi, i = 1, 2,…, n, it is easy to see that