2006-09-27 10:58:00 · 2 answers · asked by beirutzi 1 in Science & Mathematics ➔ Mathematics
One is for calculating population standard deviation (n), the other is for calculating sample standard deviation (n-1).
If you have a box of 1000 colored marbles, but you are going to draw out 100 of them for your study, then the 1000 marbles are your population, whereas the 100 that you randomly drew for your study are the sample.
2006-09-27 10:59:26 · answer #1 · answered by mim 3 · 0⤊ 0⤋
The formula for the population sd has "n" in the denominator.
The formula for the sample sd has "n-1". The reason is that the sample sd is designed to be an *estimate* of the population sd. But when you take a sample, the sample mean already deviates a but from the population mean. You would miss this deviation if you would divide by "n". Therefore, the number has to be made a little larger. This is accomplished by replacing the denominator "n" by the (slightly) smaller denominator "n-1". Precise analysis shows that this is exactly the way to get an unbiased point estimator of the population sd based on the sample.
2006-09-27 11:09:13 · answer #2 · answered by dutch_prof 4 · 0⤊ 0⤋