Error propagation
If two stochastic variables x and y are summed, subtracted, multiplied, or divided, the standard deviation σz of the result z depends on both σx and σy. This is called error propagation.If the variables x and y are not correlated, it can be shown that in case z = x+y and z = x-y:
(σz)2 = (σx)2 + (σy)2
and in case z = x·y and z = x/y:
(σz / z)2 = (σx / x)2 + (σy / y)2
In words: for addition and subtraction, the standard deviations should be added quadratically, and for multiplication and division, the relative standard deviations should be added quadratically.