Graph of the Normal Distribution
The normal distribution is specified by a mathematical rule. In the figure both the rule and the graph generated by that rule are shown. The symbols m and s are the parameters of the distribution. m is the mean of the distribution, and s is the standard deviation.
Once the parameters are known, the distribution is completely specified. It can be shown, although we will not do so (yet) that a good guess or estimate for m is the mean of the observed values. An estimate for s is the standard deviation. Although the standard deviation is a positive number, the mean can assume any value. The distribution is symmetrical with mean, mode, and median all equal at m. It is interesting to note that the exact specification of the figure shown here was taken from the German 10 DM banknote. The mean equals three, and the standard deviation equals one in this example. On the back of the banknote is a portrait of Gauss.
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