Mathematics for Chemistry/Statistics

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