Maths question

[Sigh]

I'm racking my brains over this one - If A x B = C, should the average of A x the average of B = the average of C? I think logically it should but I can't make it work exactly in my spreadsheet.

 

[GlennUK]

I don't think that mathematically, that is true.

 

[Joe4]

Absolutely not, because of the multiplication, it is creating "weighted" averages.

You can prove this with a simple example:

A x B = C

1 x 100 =100
1 x 2 = 2
10 x 0 = 0

Average of A = 4
Average of B = 34
Average of C = 34

4 x 34 does not equal 34.

 

[RoryA]

No. They are not related in that way.

 

[Andrew Poulsom]

What are A, B and C? The average of a single value would be the same as that value.

 

[Macropod]

I'm racking my brains over this one - If A x B = C, should the average of A x the average of B = the average of C? I think logically it should but I can't make it work exactly in my spreadsheet.

Not the avergae, but the reciprocal.

If: A * B = C
then
A = 1/B * C
and
B = 1/A * C

Thus, when C=1:
A = 1/B
and
B = 1/A

 

[Andrew Fergus]

I'm racking my brains over this one - If A x B = C, should the average of A x the average of B = the average of C? I think logically it should but I can't make it work exactly in my spreadsheet.

As Joe pointed out the average of C is a weighted average. The only way you can calculate the average using the values A and B (and not C) is to average each line and sum the results, like this:

assuming you have the values :
A1 x B1 = C1
A2 x B2 = C2
A3 x B3 = C3
and n = the population = 3

The average of C = (C1 + C2 + C3) / n , which can be calculated without referring to any 'C' values like this : ((A1xB1)/n) + ((A2xB2)/n) + ((A3xB3)/n). Using your notation it would be average of A1B1 + average of A2B2 + ... + average of AnBn.

This is a weighted average, which can be calculated very easily using a sumproduct formula in Excel. But you definitely cannot use the average of A x the average of B.

Andrew

 

[Sigh]

Thank you everybody for the advice, I can stop worrying now!