Explain the relationship between absolute, relative …

• Absolute Error: The magnitude of the difference between the true value of the quantity and the individual measurement value is called absolute error of the measurement. It is denoted by |Δa| (or Mod of Delta a). The mod value is always positive even if Δa is negative. The individual errors are:

Δa₁ = a_mean - a₁, Δa₂ = a_mean - a₂, ……. ,Δa_n = a_mean – a_n

• Mean absolute error is the arithmetic mean of all absolute errors. It is represented by Δa_mean.

Δa_mean = (|Δa₁| + |Δa₂| +|Δa₃| + …. +|Δa_n|) / n =

      For single measurement, the value of ‘a’ is always in the range a_mean± Δa_mean

                So, a =  a_mean ± Δa_mean Or a_mean - Δa_mean< a <a_mean + Δa_mean

• Relative Error: It is the ratio of mean absolute error to the mean value of the quantity measured.

Relative Error = Δa_mean / a_mean

• Percentage Error: It is the relative error expressed in percentage. It is denoted by δa.

δa = (Δa_mean / a_mean) x 100%