ThmDex – An index of mathematical definitions, results, and conjectures.
Endpoint bounds for real arithmetic mean
Formulation 0
Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
Then \begin{equation} \min(x_1, \dots, x_N) \leq \frac{1}{N} \sum_{n = 1}^N x_n \leq \max(x_1, \dots, x_N) \end{equation}
Proofs
Proof 0
Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
This result is a particular case of R3545: Endpoint bounds for real convex combination. $\square$