# How to calculate standard deviation on percentages?

The variance on the difference between two random variables can be calculated as: Var(X-Y) = sigma^2_X - sigma^2-Y - 2 Cov(X,Y). Numerically, i got the following values:

sigma^2_X = 0.03 (3%)

sigma^2_Y = 0.05 (5%) Cov(X,Y) = 0.00025

Calculation:

Var(X-Y) = 0.03^2 + 0.05^2 - 2 * 0.00025 = 0.0029

However, I get another result if I multiply by 100 %

3^2 + 5^2 - 2 * 0.00025 = 33.9995

How do I calculate this correctly?

• "$Y = 40 \% , X = 60 \%$". What is the meaning of that ? – callculus Oct 19 '16 at 16:51
• I deleted it. I wrote it on accident. – DBE7 Oct 19 '16 at 16:53
• And what next ? – callculus Oct 19 '16 at 17:13
• Notice that the square of $3\%$ is not $9\%$. – Michael Hoppe Oct 19 '16 at 18:17

## 1 Answer

It is true that $Var(X-Y)=Var(X)+Var(Y)-2cov(X,Y)$.

Thus $Var(X-Y)=0.03+0.02-2\cdot 0.00025=0.0495$

There is no need to multiply anything by 100. Also 0.02 and 0.03 musn´t be squared, because they are already the values of the variances.