middelkvadrert

Middelkvadrert is a term whose meaning varies by context, but in many Nordic linguistic contexts it literally means the square of the mean (mean squared). It is not a standard term in English-language statistics, and its precise interpretation should be clarified from the surrounding text. The most common mathematical reading is the square of the arithmetic mean of a set of numbers.

Formally, for a finite dataset x1, x2, ..., xn, the mean (or average) is μ = (1/n) Σ xi. The mean squared is then μ^2 = ( (1/n) Σ xi )^2. This quantity is distinct from the mean of squares, which is m2 = (1/n) Σ xi^2. The relationship between the two is used in variance calculations: Var(X) = E[X^2] − (E[X])^2, i.e., the mean of the squares minus the square of the mean.

Example: consider the dataset {2, 4, 6}. The mean is μ = 4, so the mean squared is μ^2 = 16. The mean of squares is m2 = (4 + 16 + 36)/3 = 56/3 ≈ 18.67. The variance is m2 − μ^2 ≈ 2.67.

In practice, middelkvadrert should be distinguished from the square of the mean and from the mean of squares. The former is a single scalar derived from the mean; the latter is another moment, used alongside the mean to compute variance and higher moments. Usage varies by language and field, so clarifying notation is advised.

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