Differentiate between absolute error and relative error
Answers
There are two types of error that are affected by the accuracy of measuring tools. The absolute error is defined as the absolute value (or magnitude) of the difference between the measured value and the true value. Thus, let:
ea = the absolute error
xm = the measured value
xt = the true value
The formula for computing absolute error is:
ea = | xm - xt |
There's only one catch - we don't usually know what the true value is. In that case, we just need to think about the accuracy of the measuring tool. Let's use Dan's measuring tape as an example. It is accurate to 1 inch, which means that the true value of any measurement could be up to half an inch smaller or half an inch larger than the actual measurement. The maximum possible difference between the measurement and its true value is half an inch. Therefore, the absolute error is 0.5 inches.
Diagram depicting the absolute error of the measuring tape
Absolute error of a measurement
Relative Error
There is another type of error that is affected by the accuracy of measuring tools. The relative error is defined as the absolute error relative to the size of the measurement. All you need to do is divide the absolute error by the measured value. In addition to the variables, let:
er = the relative error
Then the formula for computing relative error is:
er = ea / xm