Symmetric Distributions

Symmetric Distributions

A symmetric distribution is one where the left and right hand sides of the distribution are roughly equally balanced around the mean.The histogram below shows a typical symmetric distribution.

For symmetric distributions, the mean is approximately equal to the median.The tails of the distribution are the parts to the left and to the right, away from the mean.The tail is the part where the counts in the histogram become smaller.For a symmetric distribution, the left and right tails are equally balanced, meaning that they have about the same length.

The figure below shows the box and whisker diagram for a typical symmetric data set.

Another property of a symmetric distribution is that its median (second quartile) lies in the middle of its first and third quartiles.Note that the whiskers of the plot (the minimum and maximum) do not have to be equally far away from the median.In the next section on outliers, you will see that the minimum and maximum values do not necessarily match the rest of the data distribution well.