Explain Absolute Error, Relative Error and Percentage Error.

Explanation

(a) Absolute Error:
The magnitude of the difference between the individual measurement and the true value of the quantity is called the absolute error of the measurement.
It is denoted by `|Deltaa|`.
In absence of any other method, we consider arithmetic mean as true value.
Consider physical quantity.a. Its measurement bе `a_(1),a_(2),a_(3),....a_(n)`
`:.a_("means")=(a_(1)+a_(2)+a_(3)+...a_(3))/(n)`
Or
`=(overset(n) underset(i=1)suma_(i))/(n)` where i=1,2,3,...n
(b) Absolute error in measurement
`Delta a_(1)=a_(1)-a_("mean")`
`Deltaa_(2)=a_(2)-a_("mean")`
`: : :`
`Deltaa_(n)=a_(n)-a_("mean")`
`Delta_(a)` may be positive or negative.
Average absolute error is denoted by
`(Deltaa)_("mean")`
`=(|Deltaa_(1)|+Delta_(2)|+....|Deltaa_(n)|)/(n)`
`=(underset(i=1)overset(n)sum|Deltaa_(i)|)/(n)`
where `i=,1,2,3,4...n`
Physical quantity is represented as,
`a=a_("mean") +- (Deltaa)_("mean")`
OR `a_("mean") -Deltaa_("mean") le a le a_("mean")+Deltaa_("mean")`
Relative Error or Fractional Error:
Ratio of average absolute error `(Delta_("mean"))` and average value `(Deltaa_("mean"))` is called relative error or fractional error (relative error). It is denoted by `delta`
`:. delta=(Deltaa_("mean"))/(a_("mean"))`
(d) Percentage Error:
When relative error is expressed in terns of percentage it is called percentage error. .Percentage error = ` deltaa xx 100% `
`=(Deltaa_("mean"))/(a_("mean"))=xx100%`
here is no unit of relative error or fractional error.