Difference between Absolute and Relative error
Absolute error
1) An absolute error helps us to find the most probable value of measurement of physical quantity.
2) The magnitude of the difference between mean value and each individual value is called absolute error in the observations.
3) To find absolute error one has to find the mean value of recorded values.
4) Suppose that in measurement of any quantity x1, x2, x3 are the reading recorded using appropriate instrument, then the mean value xm can be given as,
5) Then according to definition, the absolute error in each measured value is the magnitude of difference between each measured value and mean value.
6) The value of absolute error is always taken as positive.
7) Mean absolute error is mean of individual absolute error, which is given as,
8) From the calculation of mean absolute error, we can say that the most possible value of ‘x’ can belong to xm ± ∆xm
Relative error
1) Relative error helps us to find the actual amount of errors that are introduced in the measurement.
2) The ratio of mean absolute error to the mean value in the measurement is called as relative error.
3) To find relative error one has to calculate mean value and mean absolute error of recorded values.
4) Suppose that ∆xm is the mean absolute error and xm be the mean value in calculation, then the relative error is given as,
5) If relative error is represented in percentage form, then it is known as percentage error,
∴ Percentage error = relative error × 100%
∴ Percentage error = ∆xm/xm × 100%
6) Eg. Suppose that the in measurement of inner diameter of the pipe reading obtained using vernier calliper is l=2.00±0.05 cm, then the relative error and percentage error is given as,
∴ relative error, = 0.05/2.00
∴ relative error, = 0.025
And
∴ Percentage error = relative error × 100%
∴ Percentage error = 0.025 × 100% = 2.5%