Quick facts about the normal curve

Also called the Bell curve1 or Gaussian distribution

This page produced somewhat off-the-cuff in response to two e-mail queries.  Purists will find it oversimplified. Any basic statistics textbook would give you much more depth, but here's a quick list of features:

The normal curve is often called the Gaussian distribution, after Carl Friedrich Gauss, who discovered many of its properties.  Gauss, commonly viewed as one of the greatest mathematicians of all time (if not the greatest), is properly honored by Germany on their 10 Deutschmark bill:

You will notice the normal curve to his left:
Here the formula for the curve has been modified to shift its center to   on the x-axis, and to arrange that its inflection points are at - and +.  The factor in front arranges that the area under the curve remains equal to 1.

Other miscellany:

Some numbers from the graph of the curve:
    x -3 -2 -1 0.5 0 .5 1 2 3
    y 0.0044 0.054 0.242 0.352 0.399 0.352 0.242 0.054 0.0044
 Some areas under the curve:
horizontal interval
-1 to 1
-2 to 2
-3 to 3
area under curve for that interval
(all numbers rounded above).


1) I know the name Bell Curve currently has some distasteful associations for many
people due to a controversial book of the same title.  The name was around for
probably a century before the recent book, and will likely remain long after the book is forgotten.

Last Modified March 4, 1999.
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