Errors of Measurement

This difference in the true value and measured value of a quantity is called error of measurement.

(1) Absolute error : Absolute error in the measurement of a physical quantity is the difference between the true value and the measured value of the quantity.

Suppose a physical quantity is measured n times and  measured values be a₁, a₂, a₃, ….. a_n. The arithmetic mean of these value is 

Usually, a_m is taken as the true value of the quantity.

By definition, absolute errors in the measured values of the quantity are

………….

The absolute errors may be positive or negative .

(2) Mean absolute error : It is the arithmetic mean of the magnitudes of absolute errors in all the measurements of the quantity. It is represented by Thus

Hence the final result of measurement may be written as

This implies that any measurement of the quantity is likely to lie between and 

(3) Relative error or Fractional error : It is defined as the ratio of mean absolute error to the mean value of the quantity measured. Thus

                        Relative error or Fractional error

(4) Percentage error : When the relative error is expressed in percentage, we call it percentage error. Thus

                        Percentage error