Definition:Degrees of Freedom

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Degrees of Freedom may refer to:

Degrees of Freedom (Statistics)

The number of degrees of freedom is essentially the number of independent units of information in a sample relevant to the estimation of a parameter or calculation of a statistic.

One approach is to regard the $n$ observations as the initial data, one of which is used to determine the total or mean.

As the mean must be known before we can determine deviations from it, there are $n - 1$ degrees of freedom left to estimate the variance.

Hence, in the sense that the total is fixed, only $n - 1$ values can be assigned arbitrarily, as the remaining one is then fixed to ensure the correct total.

Degrees of Freedom (Physics)

The number of degrees of freedom of $S$ is the number of normal modes of oscillation of $S$.