Error – Units and Measurement

Error: The lack in accuracy in the measurement due to the limit of accuracy of the measuring instrument or due to any other cause is called an error. The difference between the measured value and the true value of a quantity is known as the error in the measurement.

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Error – Types of Errors, Expressions

Errors are usually classified as
1. Absolute Error
The difference between the true value and the measured value of a quantity is called absolute error. If a1, a2, a3,…, an are the measured values of any quantity a in an experiment performed n times, then the arithmetic mean of these values is called the true value (am) of the quantity.


The absolute error in measured values is given by

Δa1 = am – a1
Δa2 = am – a2
Δan = am – an

2. Mean Absolute Error
The arithmetic mean of the magnitude of absolute errors in all the measurement is called mean absolute error.

\(\overline{\Delta a}=\frac{\left|\Delta a_{1}\right|+\left|\Delta a_{2}\right|+\ldots+\left|\Delta a_{n}\right|}{n}\)

3. Relative Error or Fractional Error
The ratio of mean absolute error to the true value is error.

Realtive Error = \(\frac{\text { Mean absolute error }}{\text { True value }}=\frac{\overline{\Delta a}}{a_{m}}\)

4. Percentage Error
The relative error expressed in percentage is called percentage error.

Percentage error = \(\frac{\overline{\Delta a}}{a_{m}}\) x 100%

Units and Measurement Topics:
Measurement requires tools to provide scientists with a quantity. A quantity describes how much of something there is and how many there are.

Physical Quantities and Their Units Systems of Units
Dimensions Significant Figures
Rounding off Error
Combinations of Errors