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Statistics

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Hi,
My professor gave us the formulas for sample variance and population variance, as well as the shortcut formulas for each.

However, he said that on some of the problems, we will HAVE to use the long formula, which for population variance would be: E(x-mean)^2/N

Can someone give me an example of a problem in which I would be unable to use the shortcut formulas so that I will know when it's not appropriate to use it?

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