I understand both of these as: "The average of x", but I have a feeling they're not interchangeable.
Mathematically are they the same, or is there a difference?
2026-04-02 03:19:09.1775099949
What is the Difference Between $\left<x\right>$ and $\bar{x}$?
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$\overline{x}$ is usually the mean of a sample, so $\frac{1}{n} \sum_{i=1}^n x_i$.
$\langle x \rangle$ is not typical notation in math in general but in physics it means an average over an ensemble. This informally means adding up each possible value of $x$ weighted by its probability in the distribution of interest. This "addition" is in general described by Lebesgue integration, not summation.