I have ten measurements like this:

enter image description here

and I have calculated the sample mean E(X) = 10.03, and the average of squares E(X^2) = 100.679:

enter image description here

Now I want to calculate the sample variance. I use the formula:

sample variance = E(X^2) - (E(X))^2 = 100.679 - (10.03)^2 = 0.0781

However, when using a calculator to calculate the variance, it gives the result variance = 0.08678 instead.

What did I do wrong?

  • $\begingroup$ What computer program did you use to calculate the variance? $\endgroup$ – Herr K. Apr 21 '13 at 21:14
  • $\begingroup$ I mean I used my calculator $\endgroup$ – Chin Apr 21 '13 at 21:15
  • $\begingroup$ but is my formula to calculate the variance correct? $\endgroup$ – Chin Apr 21 '13 at 21:16
  • $\begingroup$ Sorry, I misunderstood your question. I thought 0.8678 was the value you calculated. See @WillOrrick's answer below. $\endgroup$ – Herr K. Apr 21 '13 at 21:21

You must multiply your result by $10/9$ if you want the sample variance to be an unbiased estimator of the population variance. This is called Bessel's correction.


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