[2] The most common measures of central tendency are the arithmetic mean, the median, and the mode.
Analysis may judge whether data has a strong or a weak central tendency based on its dispersion.
Depending on the circumstances, it may be appropriate to transform the data before calculating a central tendency.
In the sense of Lp spaces, the correspondence is: The associated functions are called p-norms: respectively 0-"norm", 1-norm, 2-norm, and ∞-norm.
In equations, for a given (finite) data set X, thought of as a vector x = (x1,…,xn), the dispersion about a point c is the "distance" from x to the constant vector c = (c,…,c) in the p-norm (normalized by the number of points n): For p = 0 and p = ∞ these functions are defined by taking limits, respectively as p → 0 and p → ∞.
For p = 0 the limiting values are 00 = 0 and a0 = 1 for a ≠ 0, so the difference becomes simply equality, so the 0-norm counts the number of unequal points.
This perspective is also used in regression analysis, where least squares finds the solution that minimizes the distances from it, and analogously in logistic regression, a maximum likelihood estimate minimizes the surprisal (information distance).
For unimodal distributions the following bounds are known and are sharp:[4] where μ is the mean, ν is the median, θ is the mode, and σ is the standard deviation.