Why does one divide by N - 1 rather than by N when estimating a population standard deviation from the sample standard deviation?
A) Because the sample standard deviation is likely to be an imprecise estimate, we allow the error of the estimate (the standard deviation) to be larger by dividing the sum of squares by a smaller number.
B) The sample standard deviation is a superior estimate of the variability in the population than is the population standard deviation.
C) We typically have to throw out at least one data point in any given study, so the N - 1 allows us to account for that.
D) Because the population is always smaller than the sample, we must divide by a smaller number.

Question

Quizplus · Accepted Answer

Dividing by N - 1 instead of N corrects for the bias in the sample standard deviation and makes it an unbiased estimator of the population standard deviation. This is necessary because the sample standard deviation is likely to be an imprecise estimate, and dividing by N - 1 allows for a larger margin of error in the estimate.

Why Does One Divide by N - 1 Rather Than