When you want to multiply or divide average values
reported with their standard deviations, you don't simply add the standard deviations to produce the
final standarddeviation. Instead, you square the fractional standard deviations, add them, then take the square root of the sum to get the fractional
total deviation. If you have values A +- dA, B +- dB, ... and want to compute X = A*B*..., the total error
dX is then
- dX/X = sqrt( (dA/A)2 + (dB/B)2 +...)
Note that you will add the
squares of the errors even if you are dividing the actual values.
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