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### Calculating Percentage Errors

```
Date: 02/20/99 at 17:40:01
From: Brandy
Subject: Error calculation

I need to know how to calculate percent error from a set of data. The
data include predicted values and observed values. How do I basically
determine percent error?

Thanks!
```

```
Date: 02/21/99 at 06:28:41
From: Doctor Mitteldorf
Subject: Re: Error calculation

The surefire way is to do your calculation twice, once for a maximum
and once for a central value. For example

(3 +/- 0.1) + (7 +/- 0.1) / (0.9 +/- 0.1)

First you do the central value:  (3+7)/.9 = 11.1

Then you get a high value. Do this by choosing the HIGHEST value in
the numerator and the LOWEST in the denominator:

(3.1+7.1)/0.8 = 12.75

So, you'd quote the result as 11.1 +/- 1.6

-------------------------

There are more sophisticated ways to approach this, too. For any
numbers that add or subtract, you can add their absolute errors. For
any numbers that multiply or divide, you can add their percentage
errors and then turn them back to absolute errors at the end.

Another variation: if the errors in the different constituent numbers
are independent, it may be justifiable to add them "quadratically" as
the square root of the sum of the squares, rather than as the straight
sum. The meaning of this is, essentially, that if you have a lot of
numbers you are adding up, it is unlikely that you erred to the high
side on all of them. Rather, you can expect some cancellation in the
errors, so the uncertainty in the end is not as great. For example,

(2 +/- .1) + (3 +/- .1) - (4 +/- .2)

The central value is 2 + 3 - 4 = 1

The error is sqrt(.1^2 + .1^2 + .2^2) = .24

You should quote the answer as 1.0 +/- .24

- Doctor Mitteldorf, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Statistics

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