They have a nearly spherically symmetric distribution, while the density of stars decreases with increasing distance from the core.

They may have a less symmetric distribution and may be associated with pain and tissue loss.

Using the mean provided the best power for symmetric, moderate-tailed, distributions.

A histogram of the data should provide evidence as to whether the data can be reasonably modeled with a symmetric distribution.

A very common special case is the symmetric Dirichlet distribution, where all of the elements making up the parameter vector have the same value.

Unfortunately is, nevertheless, generally biased (although it obviously has the correct expected value of zero for a symmetric distribution).

The median and the mean (if it exists) of a symmetric distribution both occur at the point about which the symmetry occurs.

If a symmetric distribution is unimodal, the mode coincides with the median.

Every measure of skewness equals zero for a symmetric distribution.

Several well-known, unimodal and symmetric distributions from different parametric families are compared here.