Let $G$ be a finite groups and $n$ be a positive integer. Define $$X_n(G):=\{x\in G: x^n=1\}$$ Does there exist a positive integer $n$, such that $$\left\{\frac{|X_n(G)|}{|G|}: G\,\text{is a finite group}\right\}=\mathbb Q\cap[0,1]$$ where $\mathbb Q$ is the set of rational numbers?