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When calculating a sample variance a factor of (N-1) appears instead of N (see http://en.wikipedia.org/wiki/Sample_variance#Population_variance_and_sample_variance ). Does anybody have an intuitive way of explaining this to students who need to use this fact but maybe haven't taken a statistics course?

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    This is essentially a duplicate of [Sample Standard Deviation vs. Population Standard Deviation](http://math.stackexchange.com/questions/15098/sample-standard-deviation-vs-population-standard-deviation).2011-09-01
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    But the answer there just says that there is a bias and here's how you correct it. Is there a way to explain the correction intuitively (yes that's a little vague).2011-09-01
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    There is an attempt at an intuitive explanation in the second part of that answer. Does that help?2011-09-01
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    The concrete example I cite in my answer below can be understood without even using algebra.2011-09-01
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    The fact that correction for bias can sometimes be a very bad thing to do seems not widely understood among non-statisticians, including some who teach statistics. In this example of estimating variance, by the usual mean-squared error criterion, and assuming the sample is from a normally distributed population, the unbiased estimator is only slightly worse than the biased estimator, so it's not a good example to illustrate that point. But the idea that it is the unbiased estimator that is worse may fail to be as widely appreciated as it could be.2011-09-01

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