I'd like to add data from Census.gov, but I don't know how to add up the Margin of Error. Example, I have the estimate number of renters in Congressional District 1, (203,941 +/- 4,892) and the same data for Congressional District 2 (219,393 +/- 4,815). So, is the estimate for District's 1 & 2 equal to 423,334 +/- 9,707?

EDIT: I looked harder and found a website that is very specific. It says to take the square root of the sum of the squares. E.g., (sqrt(4815^2)+(4892^2))=6,864.

Sorry for the simple question.

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#### Best Answer

Look up "error propagation" in interweb. In your case, it's Ok to simply add the errors. However, sometime folks do the square routine: $$e_{x+y}=sqrt{e_x^2+e_y^2}$$

If you look at the Maclaurin expansion of this thing it's: $$e_{x+y}approx e_x+e_y$$, i.e. a simple sum of errors.

If for some reason you believed that the errors were correlated, then you could include correlation coefficient: $$e_{x+y}=sqrt{e_x^2+e_y^2+2rho e_xe_y}$$ However, in your case there's no reason to believe in correlation, and even if you did then you wouldn't know $rho$ anyways.

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