Relative error is a measure of the difference between an estimated or calculated value and the true or exact value. It is expressed as a percentage or decimal, and is used to evaluate the accuracy of a measurement or calculation.
Relative error is calculated by taking the absolute value of the difference between the estimated value and the true value, then dividing it by the true value and multiplying by 100 to get a percentage. The formula is (|estimated value - true value| / true value) * 100.
Absolute error is the numerical difference between the estimated value and the true value, while relative error is the ratio of this difference to the true value. Absolute error is expressed in the same units as the measured quantity, while relative error is expressed as a percentage or decimal.
Relative error is important because it allows us to assess the accuracy of our measurements and calculations. It helps us understand how much our results deviate from the true value and can guide us in making improvements to our methods and equipment.
Yes, relative error can be negative. This occurs when the estimated value is greater than the true value, resulting in a negative difference. However, when calculating the percentage error, the absolute value of the difference is used to ensure a positive value is obtained.