# Thread: Subtracting two numbers with standard deviations

1. ## Subtracting two numbers with standard deviations

I'm doing some data analysis and I have to subtract two numbers with standard deviations. The numbers are 27.03 + 0.06 and 22.66 + 0.08. The paper I'm getting the data from reports an answer of 4.37 + 0.10. Obviously 4.37 is what you get from subtracting the averages, but how does one calculate the std dev? Thanks in advance

2. Ok, I found the answer to my own question. For anyone interested, use standard error of propagation. You can do this by either adding the absolute values of the std devs or using by adding the squares of the std devs and then taking the square root. This last method was the one I was looking for.

3. Originally Posted by jmmathieu
Ok, I found the answer to my own question. For anyone interested, use standard error of propagation. You can do this by either adding the absolute values of the std devs or using by adding the squares of the std devs and then taking the square root. This last method was the one I was looking for.

The standard deviation of the difference of two random variables is the square
root of the sum of the squares of the standard deviations.

RonL

4. Isn't that what I just said above or is it somehow different? Sometimes basic math eludes me

5. Originally Posted by jmmathieu
Isn't that what I just said above or is it somehow different? Sometimes basic math eludes me

"You can do this by either adding the absolute values of the std devs.."

is not the same thing as:

"the square root of the sum of the squares of the standard deviations"

RonL

6. Oh haha, didn't mean to imply they were the same thing. Obviously not, but both are methods for standard propagation of error. Found both as answers in a text book and the authors suggested to use the latter method. Thanks for the reply though.

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# how to add two values with standard errors

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