What do you mean by absolute error, mean absolute error and relative error? State its expression.
Answers
Answer:
Explanation:
Absolute Error Formula
If x is the actual value of a quantity and x0 is the measured value of the quantity, then the absolute error value can be calculated using the formula
Δx = x0-x.
Relative Error
The relative error is defined as the ratio of the absolute error of the measurement to the actual measurement. Using this method we can determine the magnitude of the absolute error in terms of the actual size of the measurement. If the true measurement of the object is not known, then the relative error can be found using the measured value. The relative error gives an indication of how good measurement is relative to the size of the object being measured.
If x is the actual value of a quantity, x0 is the measured value of the quantity and Δx is the absolute error, then the relative error can be measured using the below formula.
Relative error = (x0-x)/x = (Δx)/x
An important note that relative errors are dimensionless. When writing relative errors it is usual to multiply the fractional error by 100 and express it as a percentage.
Mean Absolute Error
The mean absolute error is the average of all absolute errors of the data collected. It is abbreviated as MAE (Mean Absolute Error). It is obtained by dividing the sum of all the absolute errors with the number of errors. The formula for MAE is:
