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Subsection A.1.1 Means and Averages
Definition A.1.1 Arithmetic Mean.
For a collection of real-valued numbers,
\(x_1, x_2, \dots, x_n \in \mathbb{R}\text{,}\) the
arithmetic mean \(\bar{x}\) is defined as:
\begin{equation*}
\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i \, .
\end{equation*}
Definition A.1.2 Geometric Mean.
For a collection of non-negative real values,
\(\mathbf{x}=\left(x_1, x_2, \dots, x_n \right) ,
\quad x_i\in\mathbb{R}^{\geq 0} \quad \forall i\in\{1,\dots , n\}\text{,}\) the
geometric mean \(g(\mathbf{x})\) is defined as
\begin{equation*}
g(\mathbf{x}) = \left( \prod_{i=1}^n x_i\right)^{1/n} \, .
\end{equation*}
