Question

Anyone having conceptual intution behind degrees of freedom? Y do we divide by n-1 in standarad deviation?

Answer 1

Yes, here, i have seen some professors even say just use n. But basically n-1 is standard. Here is a more beginner level reasoning i would agree with. https://scholar.vt.edu/access/content/user/wilkins/Public/IMT.pdf

Answer 2

explains it perfectly. if you have questions just ask

Answer 3

http://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)

Answer 4

Hi chem Engineer, thanks for the useful article you have posted. Sorry i replied to your article very late. There was some problem with my internet connection.

The explanation gave in the article is good. That is with sampling we can easily know that sample variance gives correct answer when we divide by n-1. But it does not answer my question that, why does we have to divide by n-1. That is what is the theory or any proof behind it.

One of the intution which i have is that , suppose we have sample of 5 elements, and as we know the mean of sample . So the random variables free to vary will be only 4. And fifh one will be simply (5* mean -(sum of first four elements)). So we have 4 degrees of freedom, and hence we divide by n-1. But yet this intution is not crystal clear.

So if you have anything else to discuss, please tell

Answer 5

Hi kropot, thanks for link.degrees of freedom has a big role in deciding value of n. But y only divide by n-1, and not by any other number ? this is little confusing for me

Answer 6

http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1008&context=imseteach