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# MEI S1 Statistics: why use rmsd to find sd? watch

1. Definition of Variance of a given list of data is : Sum[ x - x(bar) ]^2 /n

And standard deviation (small case sigma) for a set of data is sqrt(Variance)

So .... why does MEI insist on using s (not sigma) = sqrt (sxx/(n-1)) ?????

Anyone?
2. Sorry you've not had any responses about this. Are you sure you've posted in the right place? Here's a link to our subject forum which should help get you more responses if you post there.
3. It's to unbias the estimator :P
To figure the sd of a population when you have the respective data for the entire population is to just apply the "normal formula" (square-rooting the average of the deviations from the mean squared)
Yet when trying to figure (more precisely, estimate) the sd of the population from a mere sample you can't just apply this "normal formula" directly to said sample because it will be biased. Just think about the average: it'll be "closer" to the sample data and yield a slightly smaller variance than if you had the actual average for from the population.

How do you account for this bias? Simply put: subtracting 1 from n in the denominator in the formula will fix this pretty neatly.
4. (Original post by Youcan)
It's to unbias the estimator :P
To figure the sd of a population when you have the respective data for the entire population is to just apply the "normal formula" (square-rooting the average of the deviations from the mean squared)
Yet when trying to figure (more precisely, estimate) the sd of the population from a mere sample you can't just apply this "normal formula" directly to said sample because it will be biased. Just think about the average: it'll be "closer" to the sample data and yield a slightly smaller variance than if you had the actual average for from the population.

How do you account for this bias? Simply put: subtracting 1 from n in the denominator in the formula will fix this pretty neatly.
Thanks, youcan
I get this, and know already about stats/unbiased estimators for whole populations versus samples from a population. Mostly, these types of questions (in an exam) would concern/use CLT, also.

My question was : for a GIVEN set of data, in order to work out the standard deviation FOR THAT SET OF data, when the question asks for standard deviation, FOR THAT SET of data, why use rmsd? Surely using rmsd is WRONG in this case?! Your first sentence seems to agree with me?!

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Updated: March 8, 2018
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