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Question

What is absolute error, mean absolute error and relative error?


Solution

Absolute error - The difference between true value (usually mean value) and measured value is called an absolute error.
Mean absolute error - (only magnitude of $$\Delta a$$
$$a= a_{mean} \pm \Delta a_{mean} \implies $$ a lies between $$a_m - \Delta a_{mean}$$ to $$a_m + \Delta a_{mean}$$
$$\Delta a_{mean} = \dfrac{|\Delta a_1| + | \Delta a_2| + ........|\Delta a_n|}{n}$$
Relative error $$= \dfrac{\Delta a_{mean}}{a_{mean}}$$
   Relative $$\% = \pm \dfrac{\Delta a_{mean}}{a_{mean}} \times 100 = fractional \ error \times 100$$

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