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Absolute error = Actual value – Measured value
To calculate the absolute error, it will be essential to know what is considered the real value. When you have a set of measurements, the real value is considered to be the mean of that set of values. In turn, the absolute value can be positive or negative, depending on whether the actual measurement is higher or lower than the measured value. Despite this, the value is always taken as positive.
Absolute error = |Actual value – Measured value|
Let’s see an example of calculating the absolute error. If we take the measurement of a child’s height as an example, in a doctor’s office what we consider to be the real value is obtained, for example 121.2 cm. If we measure the height of the child at home, suppose we get a measured value of 120.5 cm. In that case, the absolute error would be:
Absolute error = |121.2 cm – 120.5 cm|= 0.7 cm
relative error
The relative error is used as a reference for the precision of a measurement, that is, to have an idea of how true a measurement can be. It can also be considered that this error puts into perspective to what extent said error influences a measurement, since an error of one centimeter in a measurement of five kilometers does not affect the same as an error of one centimeter in a measurement of five centimeters. .
The value of the relative error can be obtained, comparing the absolute error with the real value of the property that is being measured; thus, it is the ratio between the absolute error, that is, the difference between the measurement and the true value, of a measurement and the actual measurement.
The relative error, therefore, aims to show the quality of a measurement. When making a measurement, the quality is higher the smaller the relative error.
Continuing with the previous example, the relative error can be measured as the quotient of the absolute error between the real value in percent.
Relative error = |Actual value – Measured value| / Actual value = Absolute error / Actual value (as a percentage)
Relative error = (|121.2 cm – 120.5 cm|/ 121.2 cm) 100 = 0.57%
The relative error is expressed as a percentage, and has no units, that is, it does not matter if the length, weight or temperature is being measured, since the units do not influence the result.
Example of application of both errors
Having clear the concepts of absolute and relative error, if we have a measurement of length that is equal to 12.5 ± 0.05 m, the absolute error would be 0.05 m, while the relative error would be the quotient 0.05 m/12.5 m multiplied by 100, that is, 0.4%.
Sources
- Absolute and Relative Errors. (2021). Retrieved 6 March 2021, from https://www.physicalab.com/apartado/absolute-relative-errors
- Relative Error: Definition, Formula, Examples – Statistics How To. (2016). Retrieved 6 March 2021, from https://www.statisticshowto.com/relative-error/
