Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
Let $\lambda_1, \dots, \lambda_N \in [0, \infty)$ each be an D4767: Unsigned real number such that

(i)	\begin{equation} \sum_{n = 1}^N \lambda_n = 1 \end{equation}

Then

(1)	\begin{equation} \sum_{n = 1}^N \lambda_n x_n \geq \min(x_1, \dots, x_N) \end{equation}
(2)	\begin{equation} \sum_{n = 1}^N \lambda_n x_n \leq \max(x_1, \dots, x_N) \end{equation}