LIS 504 - The normal distribution

The normal distribution is an ideal or theoretical distribution to which many actual distributions approximate, more or less.

For example, if you take a number of random samples from a population and form a distribution of the means of the samples for some variable, you will often get something close to the normal distribution.

Typically, something close to a normal distribution is produced by adding the results of a number of independent events over a large number or trials; for example, repeating n flips of a coin many times.

There are four ways a coin can land in 2 flips, and, if the flips are fair, each of these is equally likely:
# Flips Number of heads
1 0
2 1
3 1
4 2

Because each way the coin can land is equally likely, we would expect on average to see the results appear as follows over a long series of trials:
Number of heads

As we increase the number of coin tosses per trial, the shape of the normal curve begins to emerge. For example, at four tosses, we have
Number of heads
and, at 10 tosses, we have
Number of heads


Last updated November 1, 2000.
This page maintained by Prof. Tim Craven
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Faculty of Information and Media Studies
University of Western Ontario,
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