# Relative error

• Aug 8th 2010, 07:02 AM
Stuck Man
Relative error
To calculate a relative error my book says to divide the error bound by the rounded mid-value. Later a question has answers where the relative error must have been calculated from dividing the accurate mid-value by the maximum absolute error. There is often a difference of 0.05% or so between these methods. I don't know which method to use.
• Aug 8th 2010, 08:05 AM
HallsofIvy
Quote:

Originally Posted by Stuck Man
To calculate a relative error my book says to divide the error bound by the rounded mid-value. Later a question has answers where the relative error must have been calculated from dividing the accurate mid-value by the maximum absolute error.

You have this reversed, don't you? Divide the max absolute value by the "accurate mid-value" rather than the other way round.

Quote:

There is often a difference of 0.05% or so between these methods. I don't know which method to use.
Well, the only reason to have an "error" is because you don't know the actual value (which is what I think you mean by the "accurate mid-value". If you know it, then, sure, use it. But most of the time you don't so you must an estimated value. In that case, all you can do is estimate the error, anyway.
• Aug 8th 2010, 08:40 AM
Stuck Man
You can see what I mean with this example. If the relative error % is calculated by dividing 0.02324 by 15.3188725 it is 0.15%, quite different to 0.2%.
• Aug 8th 2010, 10:35 AM
Stuck Man
To answer my own question I have to look at what the question is asking for. Part c asks for the relative error in giving the value as N. Some questions ask for the relative error in the maximum absolute error compared to the mid-value.