Absolute and relative error

Compute the absolute and relative errors in using c to approximate x.

x = e; c = 2.718

Problem 10E

Absolute and relative error Compute the absolute and relative errors in using c to approximate x.

x = e; c = 2.718

Answer

Step-1

Absolute Error Formula

Absolute error is defined as the magnitude of difference between the actual and the individual values of any quantity in question.

Say we measure any given quantity for n number of times and a1, a2 , a3 …..an are the individual values then

Arithmetic mean am = [a1+a2+a3+ …..an]/n

am= [Σi=1i=n ai]/n

Now absolute error formula as per definition =

Δa1= am – a1

Δa2= am – a2

………………….

Δan= am – an

Mean Absolute Error= Δamean= [Σi=1i=n |Δai|]/n

Note: While calculating absolute mean value, we don't consider the +- sign in its value.

Relative Error or fractional error

It is defined as the ratio of mean absolute error to the mean value of the measured quantity

δa =mean absolute value/mean value = Δamean/am

Example ; what are the absolute and relative errors of the approximation 3.14 to the value ?

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