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.