The normal distribution is an approximation to the distribution of values of a characteristic. The distribution is useful as a model for the length of certain animals, the distribution of IQ scores, and so on. The exact shape of the normal distribution depends on the mean and the standard deviation of the distribution. The standard deviation is a measure of spread and indicates the amount of departure of the values from the mean.

Differences in standard deviation models the shape of the distribution. Although the distribution remains symmetric, the distribution becomes flatter if we increase the standard deviation. This corresponds to more diversity between the observations. In the animation we change the standard deviation of the normal distribution from 2.5 to 1, whereas the mean is not changed. Thus, because the standard deviation is a measure of variation, the differences between the values of the distribution decreases. Although the range of values in the movie differs dramatically, changes in standard deviation do not affect the mean, and changes in the mean do not affect the standard deviation.

Quicktime clip: changing the mean of the normal distribution |