Absolute Error

Description:

The magnitude of the difference between the true value of the quantity and the individual measurement value is called the absolute error of the measurement.

Absolute error = Measured value - True value

Consider a physical quantity is measured by taking repeated number of observations say a₁, a₂, a₃, a₄ ………a_n

Measured values = a₁, a₂, a₃, a₄,……………,a_n

True value = a₁ + a₂ + a₃ + a₄ + ... + a_n/n

Then the errors in the individual measurement values are

Δa₁ = a_mean - a₁,

Δa₂ = a_mean - a₂,

...............

Δa_n = a_mean - a_n

The arithmetic mean of all the absolute errors is the mean absolute error of the value of the physical quantity.

Mean absolute error = (|Δa₁| + |Δa₂| + |Δa₃| + ... + |Δa_n|)/n

Δa_mean = ∑ |Δa_n|/n