X1.1 question - sample standard deviation

[Revelation]

Hi all,

The terminology of Assignment question X1.1 confused me:

It describes the sample standard deviation of a sample of 20 as being £500.

However, the solution shows that this has been calculated as the sum of the square residuals with a denominator of 20, rather than the denominator of 19 I would have expected.

I'm entirely confident on the mathematics of this point as I covered it in my maths degree (and it's summarised on http://en.wikipedia.org/wiki/Standard_deviation#Estimating_population_standard_deviation).

However, does anyone have a steer on how the examiners tend to treat this sort of point?

Thanks

 

[Calum]

Caveat: my knowledge of stats is limited! If I recall correctly, using n-1 instead of n is only necessary for small sample sizes (as the difference becomes small as n increases). I wonder therefore if treatment of this point has simply been dropped from the syllabus on the grounds that real world applications are likely to only involve large n?

 

[John Lee]

Hi all,

The terminology of Assignment question X1.1 confused me:

It describes the sample standard deviation of a sample of 20 as being £500.

However, the solution shows that this has been calculated as the sum of the square residuals with a denominator of 20, rather than the denominator of 19 I would have expected.

I'm very confused - the sample variance should have denominator (n-1) however the solution doesn't mention the denominator at all...

It simply equates the given sample variance 500² to the model variance var(X).

Just to confuse matters further - with the method of moments you can equate either the "n denominator" or the "n-1" denominator variance formulae to the model variance var(X).