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If I were to explain degrees of freedom in layman terms (without using any statistical jargons) how do I do it?
Also, can someone help me understand as to why (n-1) is used instead of n in the denominator while computing standard deviation.I did go through the reasoning posted on a few forums (that it has to do with degrees of freedom and depends on whether data is from a sample or the population itself) but did not completely understand it.Most statistical books conveniently give a brief explanation which is not complete and say that it is beyond scope!
to get an unbiased estimation of the standard deviation you have to divide by n-1. You get an explanation why in http://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
Hope this helps,
Imagine i ask u to choose 5 numbers that sum up to 100.
For simplicity sake u tell me the 5 no.s are 20, 20, 20, 20, 20.
But when you utter 20 fourth time, i tell you to stop and ask you what was our goal
you tell me that the goal was to choose 5n.o s that sum up to 100. So at this point i ask you how much total we have. you reply we have 80. So to get to 100, i ask how much more we need.
You tell me that is simple 100 -80 = 20, i.e another 20.
So here in this case u had degree of freedom to choose only 4 numbers i.e (20,20,20,20). Due to the specified condition of getting 5 no.s summing upto 100, the 5th number chose itself,
hence the saying N-1. (5-1 = 4 is your degree of freedom).
Hope i could explain your query.