Error propagation

If two stochastic variables x and y are summed, subtracted, multiplied, or divided, the standard deviation σ_z of the result z depends on both σ_x and σ_y. 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:

(σ_z)² = (σ_x)² + (σ_y)²

and in case z = x · y and z = x / y:

(σ_z / z)² = (σ_x / x)² + (σ_y / 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.

Related concepts

• mean value
• standard deviation
• statistics
• stochastic variable