- #1
kotreny
- 46
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One common explanation of the concept of D.F. is this:
Suppose you have n numbers (a, b, c,...) that make up a sample of a population. You want to estimate the variance of the population with the sample variance. But the sample mean m is being calculated from these numbers, so when determining the variance ((a-m)2+(b-m)2+(c-m)2...)/n, only n-1 numbers are free to vary. The n-th number must be chosen so that the mean of all n numbers comes out to m. Thus, there are only n-1 "degrees of freedom."
But wait--shouldn't m be free to vary in this case? The value of the n-th number is a function of the other numbers and m. Fair enough, but that means m must become the n-th degree of freedom!
Suppose you have n numbers (a, b, c,...) that make up a sample of a population. You want to estimate the variance of the population with the sample variance. But the sample mean m is being calculated from these numbers, so when determining the variance ((a-m)2+(b-m)2+(c-m)2...)/n, only n-1 numbers are free to vary. The n-th number must be chosen so that the mean of all n numbers comes out to m. Thus, there are only n-1 "degrees of freedom."
But wait--shouldn't m be free to vary in this case? The value of the n-th number is a function of the other numbers and m. Fair enough, but that means m must become the n-th degree of freedom!