I'm being pedantic but, >Every distribution can be described as a curve. The width of this curve is known as its variance. Not every distribution has a varian

I'm being pedantic but, >Every distribution can be described as a curve. The width of this curve is known as its variance. Not every distribution has a variance. Some notable examples include the Cauchy distribution (or Lorentz lineshape in physics), https://en.m.wikipedia.org/wiki/Cauchy_distribution https://en.m.wikipedia.org/wiki/Cauchy_distribution the Power law distribution for powers lesser or equal to 2, https://en.m.wikipedia.org/wiki/Pareto_distribution https://en.m.wikipedia.org/wiki/Pareto_distribution and the Levy distribution, https://en.m.wikipedia.org/wiki/Lévy_distribution https://en.m.wikipedia.org/wiki/Lévy_distribution These are not mathematical curiousities but actually describe real physical systems. Additionally, the variance works as a "width" only for unimodal distributions. Any variance based metrics or analysis should only be used after checking for multimodality and, for multimodal data, with extreme caution thereafter.