Why do US and UK Schools Teach Different methods of Calculating the Standard Deviation?

As I understand UK Schools teach that the Standard Deviation is found using:

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whereas US Schools teach:

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(at a basic level anyway).

This has caused a number of my students problems in the past as they have searched on the Internet, but found the wrong explanation.

Why the difference?

With simple datasets say 10 values, what degree of error will there be if the wrong method is applied (eg in an exam)?

Answer

The first formula is the population standard deviation and the second formula is the the sample standard deviation. The second formula is also related to the unbiased estimator of the variance – see wikipedia for further details.

I suppose (here) in the UK they don’t make the distinction between sample and population at high school. They certainly don’t touch concepts such as biased estimators.

Attribution
Source : Link , Question Author : Amos , Answer Author : csgillespie

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