Let ${x}_{1},...,{x}_{25}>0$ be such that $\sum _{i=1}^{25}{x}_{i}=4350$ and $\sum _{i=1}^{25}{x}_{i}^{2}=757770.25$.

From the first equality alone, we know that at least one of the ${x}_{i}$'s must be less than or equal to $\frac{4350}{25}=174$. From the second equality alone, we know that at least one of the ${x}_{i}$'s must be less than or equal to $\sqrt{\frac{757770.25}{25}}=174.1$, which is less useful than the first bound. My question is whether we can get a better bound, i.e. to find the least upper bound of $min\{{x}_{1},...,{x}_{25}\}$, when we use both equalities together. I appreciate any comments or hints.