What is an example of a variable that is not normally distributed?

A variable that shows serious departure from the classic bell-shaped, or "Gaussian", curve is described as being not normally distributed. This departure could take the form of skew and/or kurtosis and/or multi modality.

An example might be weekly wages. If you drew a histogram of a population's earnings you would most likely see a distribution skewed significantly toward the right. That is, toward the higher incomes.

Another example is height. If you drew a histogram of a population's height you would see a bimodal distribution. One peak for males and another peak for females. The distribution of height for males and females might be normal when looked at individually, but not normal when you combine them.