PropError2

PropError2 - PROPAGATION OF ERROR Frequently it is...

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PROPAGATION OF ERROR Frequently it is necessary to combine measurements using some defined relation to obtain a property of interest. For example, a measurement of mass of an object may be combined with a measurement of its volume to determine its density. As described earlier, a measurement consists of a best estimate and an indication of its precision or uncertainty, x ± s. When measurements are combined, it is also necessary to combine their uncertainties, but in a specified manner. Table 1 summarizes the common math operations and the specified manner in which their uncertainties are to be combined. Operation z Including uncertainties s z Addition z = x + y (x ± s x ) + ( y ± s y ) = z ± s z s z = s x 2 + s y 2 Subtraction z = x - y (x ± s x ) - ( y ± s y ) = z ± s z s z = s x 2 + s y 2 Multiplication z = x * y (x ± s x )*( y ± s y ) = z ± s z s z z = s x 2 x 2 + s y 2 y 2 Division z = x / y (x ± s x )/( y ± s y ) = z ± s z s z z = s x 2 x 2 + s y 2 y 2 Exponential z = x

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PropError2 - PROPAGATION OF ERROR Frequently it is...

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