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AW: Area under Curve

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  • Subject: [mg7963] AW: [mg7943] Area under Curve
  • From: Buttgereit <Buttgereit at>
  • Date: Wed, 30 Jul 1997 02:37:26 -0400
  • Sender: owner-wri-mathgroup at

Hi Sankar,
you can use ListIntegrate[] to get your AUC. As well you could use an
InterpolatingFunction[] object and then use NIntegrate[].
Note that the result depends on the way of interpolation. Using first ord=
interpolation (straight lines between adjacent points) you would have to
calculate the sum of the areas of n-1 trapezoids (what is trivial).
If you should like to connect your points using a function like a
stair-case, your problem reduces to calculating the mean of your yi and
multiply it with your x-range (if equally spaced).
You could also fit a suitable model to your data first and then use
Integrate[] on your model.
"The Mathematica Journal" Volume 7, Issue 1 (Winter 1997) pp. 29 gives an=

example of this and shows how to estimate the error of the calculated AUC=

(given in the "In[] and Out[]" section - you might already get it on

Von:    Sankar Baruah[:]
Gesendet:       Freitag, 25. Juli 1997 11:05
An:     INTERNET:mathgroup at
Betreff:        [mg7943] Area under Curve

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From: Sankar Baruah <sankar-baruah at>
To: mathgroup at
Subject: [mg7963] [mg7943] Area under Curve
Organization: The University of Iowa

I am new to Mathematica and would really appreciate some pointers from
experienced users.  I have a 2 variable data set of about 50
observations.  I want to plot each obseravtion and calculate the area
under the curve.  How do I do this in Mathematica ?
Are there examples in the Mathematica Book and/or are there separate
application notes etc. available ?

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