# Covariance - which is correct?

Discussion in 'Mathematics' started by Informant, Nov 20, 2011.

1. ### InformantNew commenter

AQA Stats 1 textbook unambiguously states covariance is S(subscript xy) which it defines as the sum of the product of the deviations of x and y from their mean values.......divided by n.
However the AQA data booklet provided for students use in the exam defines S(subscript xy) as the sum of the product of the
deviations of x and y from their mean values (not divided by n).
This is used to find product moment correlation coefficient (pmcc), but since the denominator is handled consistently (also divide by n or don't divide by n) then pmcc formula is consistent between textbook and data booklet.
Which is correct for S(subscript xy) and do you have any suggestions on what to advise my students?

2. ### InformantNew commenter

Ah....take 2!
I now realise from another textbook that lower case S(subscript xy) is covariance as previously defined and that upper case S(subscript xy) is different but correctly defined in the data booklet. However the AQA materials appear to make no attempt to identify or explain this subtle difference.
So does upper case S(subscript xy) have a name or a useful explanation?

3. ### Polecat

You are correct that the lower case s_xy formulae give covariance, in line with the s_xx and s_yy formulae which give variance.
To quote from 'A concise course in A-level statistics' by Crawshaw and Chambers:
The 'big' S formulae are useful in calculations where the factor n cancels, but it should be remembered that they are not the formulae for covariance and variance.