Non Normal Distributions

Asymmetric Normal distributions:

The most common kind of assymetry that occurs for a normal distribution is called skewness. In this case, the median and mean are not the same. Typically, student exam scores show slight positive skewness. (Note a negatively skewed exam should be tossed out - its a poor exam).

Strong negative skewness:

Strong positive skewnewss:

Weaker positive skewness:

Sometimes the distribution is bimodal such that the mean is well below the mode(s). This can be a difficult distribution to work with but if the separation between the peaks is large, then this can be treated as the sum of two normal distributions. (e.g. height of humans = height of females plus males)

In a strongly bimodal distribution, the mean, medians or standard deviations mean relatively little. Nature, however, is usually not subject to a bimodal distribution.

However, nature does often exhibit a skewed distribution when there is a physical limit in the system. Flood stage levels are a good example as there is no such physical thing as a negative flood stage:

Negatively skewed distributions can are usually better approximated by something called the Weibull Distribution:

The Weibull Distribution applicable to wind load data (and maybe floods)

Simulator