A velocity dispersion (σ, sometimes shortened to dispersion) is the statistical dispersion of velocities of a group of objects. It is a quality of interest in open clusters, globular clusters, galaxies, galaxy clusters, and superclusters. Radial velocity can be determined by Doppler shift and the width of the affected spectral lines can determine dispersion across a group, which, with the virial theorem, can determine the group's mass. Statistical dispersion characterizes the "spread" of a distribution function and the standard deviation of a sample set is one measure of statistical dispersion.
Velocity dispersion can also be of interest regarding fluid and dust, e.g., within clouds and stars.
The term dispersion (or chromatic dispersion) is also used in optics, spectroscopy, and radio astronomy (or any type of wave such as sound waves) to indicate waves' differences in velocity through a medium when the velocity depends upon the frequency. This is used by refractive spectroscopes and also is the source of chromatic aberration in lenses.