Let $\{X_α\}$ be a family of random variables following a certain type of distributions with finite expectation $\mathbf{E}[X_α]$ and finite variance ${\rm Var}(X_α)$, where $α$ is a parameter. Motivated by the recent paper of Hollom and Portier (arXiv: 2306.07811v1), we study the anti-concentration function $(0, \infty)\ni y\to \inf_α\mathbf{P}\left(|X_α-\mathbf{E}[X_α]|\geq y \sqrt{{\rm Var}(X_α)}\right)$ and find its explicit expression. We show that, for certain familiar families of distributions, including uniform distributions, exponential distributions, non-degenerate Gaussian distributions and student's $t$-distribution, the anti-concentration function is not identically zero, while for some other familiar families of distributions, including binomial, Poisson, negative binomial, hypergeometric, Gamma, Pareto, Weibull, log-normal and Beta distributions, the anti-concentration function is identically zero.