# degress of freedom aren't explained well

#### Dio777

##### New Member
Why do we divide with n-1 instead of n, when population variance is estimated from the sample? Yes, sample will have less variability, so our estimate based on n will underestimate population variance – so if we divide with something smaller, like n-1, it will be bigger, makes perfect sense. But why n-1?? The argument is that we are getting information from only n-1 independent pieces, because the last one is already given by the mean, therefore only n-1 values are free to vary. I understand the flow of argument and clearly one can determine the last value from average, however I don’t understand how exactly it applies here. If one wanted to determine just sample variance (not as population estimate) than you would divide with n, but you only have n-1 values that are free to vary? So why doesn’t the same logic apply. Also, one can potentially estimate last value from the mean but we are not doing that. Maybe I don’t understand enough statistics yet, but please somebody explain this.

#### yupeh

##### New Member
also sometimes degrees of freedom depends on how many parameters are involved in a certain distribution or formula... like for example for the population variance, there is one parameter involved (mu - population mean) that's why we subtract one in our n (count)... or in simple terms, my prof says that it assumes or allocates the error that may be involved in computing the problem...

i am glad that you are curious with some 'ignored concepts' , since most of the students only accept what is written or taught in schools... i am very glad that you had some interest with it.. hehehe hope i answered your question

#### Tart

##### New Member
Ahh mysterious degreees of freedom

Q: What exactly is degrees of freedom?
A: The rank of a quadratic form.

Try explaingn that to an engineering student. How many of them know about quadratic forms, and that you can represend the variance in thee quadratic form?