>Why do you lose a degree when moving from population to a sample?
Because when you take sample, the statistic of the values you obtained are slightly more representative of the sample you took than representative of the population. When you try to guess the population via the sample, the result you get is influenced by the sample you used.
The degree of freedom, is n – 1, because that’s number of values that describe the population without being influenced by the sample.
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