Need help with explaining why this doesn't work...

[jste1212]

Trying to explain in the following example why you can't multipy the difference of two variances ( variance of (x/y) multiplied by variance of (y) ) to get the difference of x. I know it doesn't work, but can't explain why. Thanks!

	Set 1	Set 2	Variance
X	135	75	60
Y	15	10	5
X/Y	9.0	7.5	1.5
Y(X/Y)	135	75	7.5

 

[JeffM]

Trying to explain in the following example why you can't multipy the difference of two variances ( variance of (x/y) multiplied by variance of (y) ) to get the difference of x. I know it doesn't work, but can't explain why. Thanks!

	Set 1	Set 2	Variance
X	135	75	60
Y	15	10	5
X/Y	9.0	7.5	1.5
Y(X/Y)	135	75	7.5

This has nothing to do with variances. It is just first-week algebra.

\(\displaystyle a - b = c\) Generalizing your first row.

\(\displaystyle d - e = f\) Generalizing your second row.

\(\displaystyle \dfrac{a}{d} - \dfrac{b}{e} = \dfrac{ae - bd}{de}.\) Generalizing your third row. Remember about common denominators.

\(\displaystyle d * \dfrac{a}{d} = a.\) Generalizing first column's transition from third row to fourth.

\(\displaystyle e * \dfrac{b}{e} = b.\) Generalizing second column's transition from third row to fourth.

\(\displaystyle (d - e) * \dfrac{ae - bd}{de} = \dfrac{ade - bd^2 - ae^2 + bde}{de}.\) Generalizing third column's transition from third row to fourth.

\(\displaystyle a + b \ne \dfrac{ade - bd^2 - ae^2 + bde}{de}.\)

You had an equation in the third row. You multiplied each element of the equation by a different factor to get the fourth row. Now you do not have an equation. Multiply both sides of the equation by the same number to maintain equality.