Expected value and standard deviation Watch

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Report Thread starter 2 years ago
My teacher wanted an example of ''the mean's expected value and standard deviation'' so I sent him this which he thought was a good one! But (!) he also asked what the expected value and standard deviation will be for 16 buns? I know that the expected value will be the same but I'm not sure about the standard deviation. Help please!
If a bakery have a ''population'' of 1000 cinnamon buns and each bun weighs 50 grams (which we know since there is a machine portioning the dough) the expected value is 50 grams. But if I pick a random bun from the population, the weight can differ from the expected value with...let's say 5 grams (standard deviation) .
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Report 2 years ago
Probably your teacher was intending to point out the difference between sample and population variance.

In your example the variance is 5^2=25 which is the population figure. If you worked with a sample of 16 then before you divided by n you had 25*16=400 and you should have divided by (n-1) which gives you 400/15=26.67. The sample SD is the root of this 5.16.

The bigger your sample, the nearer the sample and populations SDs get to one another.

The reason all this happens is a bit obscure to me but the essential is this, if you take a sample from a large normally distributed population, you are more likely to get a sample that is near the mean than far away, apparently this means that the sample as a whole will be biased towards the mean. By dividing by n-1 instead of n in the variance calculation you correct for this.

Can a stats expert comment on this wikipedia entry which says

"...the sample variance is an unbiased estimator for the population variance, but its square root, the sample standard deviation, is a biased estimator for the population standard deviation."

I can't see how this can be correct but stats is so often a case of what words mean rather than what numbers mean.

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