Define and give mathematical expression for absolute error, relative error and percentage error

Question Id: PH0000001

Question: Define and give mathematical expression for absolute error, relative error and percentage error.

Solution: 

Absolute Error: The difference between the measured or inferred value of a quantity and its actual value is called the absolute error ( \(AE\) ). 

So, \(AE=V_{a}-V_{e}\) 

Where \(V_{a}\)  is approximate value and \(V_{e}\) is the exact value.

Relative Error: The ratio of the absolute error of the measurement to the actual measurement is called relative error ( \(RE\) ).

So, \(RE=\frac{AE}{V_{e}}=\left | \frac{V_{a}-V_{e}}{V_{e}} \right |\)

Percent error(\(PE\)) is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

So, \(PE=R_{e}\times 100%=^{}\frac{AE}{V_{e}}=\left | \frac{V_{a}-V_{e}}{V_{e}} \right |\times 100%\) 

∴ Above are the definition and mathematical expression . (Answer)

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