Examples of Error Propagation—Uncorrelated Variables

Examples of error propagation formulas for many common functions are given in this section. In all cases, uncorrelated variables are assumed. 

If fli = fl2 = h this example applies to the very common case of summation or difference of two variables. 

The standard error for Examples 2.14 and 2.15 takes a simpler and easy-to-remember form for both the product and the quotient if it is expressed as the relative error. It is trivial to show that 

the relative error of the product oXjXj or the quotient oxi/x2 is equal to the square root of the sum of the squares of the relative errors of the variables Xj and X2. 

There is another very important use of Eq. 2.84, which has to do with the calculation of the variation of a function in terms of changes of the independent variables. Consider again the function fix, X2.x ) and assume that the variables Xj, X2. x have changed by the amounts Axj, Ax2. Ax. The variation or change of /(xj. x ). A/, is given by 

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