14 thoughts on “Review and intuition why we divide by n-1 for the unbiased sample | Khan Academy”

  1. still dont get it. yes you would be underestimating it if u take the sample cluster below the mean. but if the cluster is above the mean? you would be overestimating it! seems arbitrary to me.

  2. So why minus – 1? Why not – 2 ? Or minus 6,345 % ? This is still not an explanation of the n – 1 :-(.

  3. If you want a more technical explanation/proof, Wikipedia Bessel's Correction. This video has some good intuition though.

  4. It has to do with the fact that on an interval with N points there are N-1 smallests subintervals. Consider for example the interval [1,4] on the natural number line in which case N=4 You can subdivide it only in [1,2] [2,3] [3,4] which is 3 not 4 smallest subintervals.

  5. The most common question seems to be why n-1 and not n-2 or n-3424342 (any other number). The way I understand it comes from the definition of unbiased estimators (look it up on wikipedia), in a nutshell an unbiased estimator is one whose expected value equals the value it is estimating. n-1 is known as bessel's correction (also on wikipedia). Here you can see that E[S^2]=sigma^2, hence it is unbiased. This makes sense; if you take enough samples and average them, you get true pop value.

  6. I GET IT! I had to work out the proof and think about it really hard, but I get it! I have an intuition for why n-1 makes sense! Message me with your questions, because I don't think I can explain it easily in the comment boxes.

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