Mathematics for Chemistry/Statistics
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Definition of errors
For a quantity the error is defined as . Consider a burette which can be read to ±0.05 cm3 where the volume is measured at 50 cm3.
- The absolute error is
- The fractional error is ,
- The percentage error is %
Combination of uncertainties
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
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
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