Sometimes we may need to do qualitative analysis of multiple Gaussian variables $\mathcal{N}(\mu_1,\sigma_1^2),\mathcal{N}(\mu_2,\sigma_2^2),\ldots$.
A naive strategy would be to just compare their means for a very coarse idea of which Gaussian is performing how.
I am interested in knowing what are the other complex ways in which a single scalar real can be attributed to $\mathcal{N}(\mu,\sigma^2)$ that can give maximum qualitative idea about a Gaussian distributed variable w.r.t. any criteria people have studied for?