Absolute Error

The absolute error E in the measurement of a quantity x is given by the equation

where x_t is the true or accepted value of the quantity. Returning to the data displayed in Figure 1-1, the absolute error of the result immediately to the left of the true value of 20.0 ppm is 20.2 ppm Fe; the result at 20.1 ppm is in error by 10.1 ppm Fe.

Figure 1-1 Results from six replicate determinations of iron in aqueous samples of a standard solution containing 20.0 ppm iron(III). The mean value of 19.78 has been rounded to 19.8 ppm

  Note that we keep the sign in stating the error. The negative sign in the first case shows that the experimental result is smaller than the accepted value, and the positive sign in the second case shows that the experimental result is larger than the accepted value.