Hi, a question about Normal Distribution: Individual items have these properties: mean=60, stddev=4. Randomly 9 items will be taken. What is the average variance of the 9 items? What is the total stddev of the 9 items?
From my knowledge, Individual items have no moments. A probability distribution has properties. Such as mean, variance ... Etc ... Which is an ensemble. It works to the limit. For infinitely many outcomes. You expect the parameters you assume. Same for 9 items. But it will be flawed. Too small is the sample. It's like coin tosses with a fair one. You expect 9/2 heads and tails as well. However time average takes trials, To match the ensemble average. If the process is Ergodic. But expect lots of black swans, If you use the bell curve for markets.
The given data is from an educational NASA contractor site: http://www.engineeredsoftware.com/nasa/normal.htm It is the last example on the page (that with the 9 batteries). It seems the question is correctly formulated, and also interesting IMO. But, because I couldn't follow some parts of their solution (there are clearly also some bugs on the page), I simplified and reformulated the question here on ET hoping to find an answer to the said 2 questions.
https://en.m.wikipedia.org/wiki/Standard_score https://en.m.wikipedia.org/wiki/Normalization_(statistics) Can't help.
I just seek an answer to the specified 2 specific questions of mine in the initial posting. I have no problems with z-scores aka normalisation etc.
My solution is: - average variance of the 9 items: (4 / sqrt(9))^2 = 1.77778 - total stddev of the 9 items: (9 * 4) / sqrt(9) = 12 I'm not sure whether the average variance calc is correct, maybe someone can confirm it. Thx.