Estimation or Calculation of Errors

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Absolute Error

The absolute error in each measured value is the difference between true value (mean value) and that measured value.

Let the Measured values in an experiment are  :

a1, a2, a3, a4, a5……...an

Then, mean or true value is

Here, amean is considered to be the true value.

Hence absolute error in each measured value is

∆a1 =  am - a1

∆a2 =  am - a2

∆a3 =  am - a3

∆a4 =  am - a4

∆a5 =  am - a5

.

.

.

∆an =  am - an

So, the Mean or Average of absolute errors is given by

Hence the true value can be written as

Relative error 

It is the ratio of average absolute error to the true value of measured quantity.

It is also known as fractional error.

Percentage error

When the relative error is expressed in terms of percentage, then it is known as Percentage Error.

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