Mathematics for Chemistry/Statistics
| A reader has identified this chapter as an undeveloped draft or outline.
You can help to develop the work, or you can ask for assistance in the project room.
Definition of errorsEdit
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 uncertaintiesEdit
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 subtractionEdit
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 divisionEdit
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