The Normal Distribution |
Introduction
Comparison
of different normal distributions
Using
Normal Tables
A
worked example
The normal distribution is the most important pattern of data that occurs in statistics.
It is a very common distribution, modelling for example the heights of people, the weights of similar animals, measurements on machine produced items etc.
There are, however, MANY continuous variables which are not even approximately Normally distributed, but they are not 'abnormal' either! For this reason the Normal Distribution is now frequently referred to as the Gaussian Distribution, named after the German mathematician Gauss (1777-1855) who derived it mathematically as the probability distribution of the error of measurements.
The reason we are so interested in the Normal Distribution is that it has a very important use in the statistical theory of drawing conclusions from sample data about the populations from which the samples are drawn, and in Statistical Process Control.
The Normal Distribution is often written as N(m , s ) where m is its mean and s is its standard deviation .
It is VERY IMPORTANT to note that :
Comparison Of Different Normal Distributions
There are of course an infinite number of Normal distributions with different means and standard deviations, but they all have the same basic properties listed above.
 |
This diagram shows
3 different normal distributions.
The first has a mean of 0 and standard deviation of 1. The second has the same mean,0, but a larger standard deviation, 2. Notice how it is flatter and more stretched out, the numbers having a greater spread. The third has the same standard deviation as the first, 1, but a larger mean, 4, so the curve is shifted along the axis. |
The STANDARD NORMAL DISTRIBUTION, which is the one in the tables we use, has a mean of 0 and a standard deviation of 1.
Using
Normal Tables
A worked example.
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Sidney Tyrrell January 2001