# Arithmetic vs Geometric Mean Consider a domain of $[0, 1]$. Let us have two functions, the arithmetic mean and the geometric mean (for now limiting the number of inputs to $2$): $f(x, y) = \frac{x + y}{2}$ $g(x,y) = \sqrt{x \cdot y}$ Now, consider the following table: |x|y|f(x,y)|g(x,y)| |------|------|------|------| |1|0|0.5|0| |0|1|0.5|0| |0|0|0|0| |1|1|1|1| We can see that the the **geometric mean** is very similar to a *logical and*, while the **arithmetic mean** is more similar to a *logical or*. --- Date: 20230516 Links to: Tags: References: * []()