Measurement is a fundamental aspect of physics and engineering. However, despite the best efforts, no measurement is perfect. There is always a difference between the measured value and the true value, which is known as the error of measurement. This topic is crucial for exams like JEE, NEET, and CBSE Class 11, as it forms the basis of error analysis in experiments.
Types of Errors in Measurement
1. Absolute Error
Absolute error refers to the magnitude of the difference between the true value and the measured value of a physical quantity.
Suppose a physical quantity is measured n times, and the measured values are: \begin{array}{l} a_1, a_2, a_3, …, a_n \end{array}
The arithmetic mean of these values is: \begin{array}{l} a_m = \frac{a_1 + a_2 + … + a_n}{n} \end{array}
This mean value is taken as the true value of the quantity if it is unknown otherwise.
The absolute error in each measurement is given by: \begin{array}{l} \Delta a_i = | a_i – a_m | \end{array} where ฮai is the absolute error for each individual measurement.
2. Mean Absolute Error
Mean absolute error is the average of all absolute errors and is given by:
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