Degrees of Freedom
Degrees of freedom is a measure of how much an estimate is able to vary.
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Mean
Given a random sample of n observations (xi) from a larger unknown population (X), the true population's mean (μ) can be estimated using the sample mean.
With the mean estimated from the sample, the sample has lost a degree of freedom. As long as the mean is fixed at this estimate, the first n - 1 observations are allowed to vary, but the nth observation is fixed at whatever value enables the mean equation to remain true.
As a result, subsequent equations making use of the estimated mean must deduct 1 from the sample size. For example, estimation of the true population's standard deviation (σ) with the sample standard deviation while making use of the sample mean.
