The measuring process is essentially a process of comparison. Inspite of our best efforts, the measured value of a quantity is always somewhat different from its actual value, or true value. 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 magnitude of the difference between the true value and the measured value of the quantity.
Let a physical quantity be measured n times. Let the measured value be \[{{a}_{1}},\,{{a}_{2}},\,{{a}_{3}},\,...\,{{a}_{n}}\]. The arithmetic mean of these value is \[{{a}_{m}}=\frac{{{a}_{1}}+{{a}_{2}}+......+{{a}_{n}}}{n}\]
Usually, \[{{a}_{m}}\] is taken as the true value of the quantity, if the same is unknown otherwise.
By definition, absolute errors in the measured values of the quantity are
\[\Delta {{a}_{1}}={{a}_{m}}-{{a}_{1}}\]
\[\Delta {{a}_{2}}={{a}_{m}}-{{a}_{2}}\]
................
\[\Delta {{a}_{n}}={{a}_{m}}-{{a}_{n}}\]
The absolute errors may be positive in certain cases and negative in certain other
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