# Mathematics for Chemistry/Statistics

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## Definition of errors[edit]

For a quantity the error is defined as . Consider a burette which can be read to ±0.05 cm^{3} where the volume is measured at 50 cm^{3}.

- The
*absolute error*is - The
*fractional error*is , - The
*percentage error*is %

## Combination of uncertainties[edit]

In an experimental situation, values with errors are often combined to give a resultant value. Therefore, it is necessary to understand how to combine the errors at each stage of the calculation.

### Addition or subtraction[edit]

Assuming that and are the errors in measuring and , and that the two variables are combined by addition or subtraction, the uncertainty (absolute error) may be obtained by calculating

which can the be expressed as a relative or percentage error if necessary.

### Multiplication or division[edit]

Assuming that and are the errors in measuring and , and that the two variables are combined by multiplication or division, the fractional error may be obtained by calculating