Question

Describe relative error,absolute error and percentage error.mathematically derive their respective formula

Answer 1

Answer

Difference between measured value and actual value is called error (∆x).

∆x = measured value - actual value.

Absolute error

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

If $\sf x_{mean}$ = actual value and $\sf x_{i}$ = $\sf x^{th}$ observed value, then the absolute error in the $\sf x^{th}$ observed value is defined as

$\sf | \Delta x_i| = |x_i - x_{mean}|$

Absolute error is always positive and has same unit as that of the quantity being measured.

Relative error

The relative error of a measured physical quantity is the ratio of the mean absolute error to the mean value of the quantity measured.

$\sf Relative \: error = \dfrac{ Absolute \: error}{ actual \: value}= \dfrac{ \Delta x_{mean}}{ x_{mean}}$

Relative error is a pure number having no unit

Percentage error

$\sf Percentage \: error = Relative \: error \times 100 = \dfrac{ \Delta x_{mean}}{ x_{mean} } \times 100$