Propagating error for an equation that uses radius, when measurements are in diameter?

Question

I'm trying to propagate standard error, however to get the number needed for the formula I'm using, I had to divide my diameter data in half to get my radius data.

Do I have to divide all of my raw data in half, calculate my mean from that, then calculate my standard deviation from there, or do I keep my data raw and somehow account for dividing by a whole number as part of my standard deviation calculations from my mean diameter data?

Answer 1

Dividing a measure by a constant divides the absolute error by the same constant. The relative error remains the same:

d = 1.0 +/- .1 cm --> r = .5 +/- .05 cm

δd/d = 10% δr/r = 10%

Isn't that nice!

Take care.