\mu

Mu

Naming convention: meaning depends on the field

In plain English

Usually the mean, or centre, of a distribution. $\mathcal{N}(\mu, \sigma^2)$ is a bell curve centred at $\mu$ . As a unit prefix, µ means "micro" (one-millionth): µm, µs. Physicists also use $\mu$ for friction coefficients, magnetic moments and chemical potential.

As code

const xs = [2, 4, 4, 5, 7];
const mu = xs.reduce((a, b) => a + b, 0) / xs.length; // 4.4

Where the analogy bends: This computes a sample mean. μ in a paper often means the true (population) mean, which a sample only estimates.

See it

μ (mean)0.00σ (std. dev.)1.10

\mu

shifts the centre and

\sigma

sets the spread. About 68% of the probability lies within one σ of μ.

What it means, field by field

Mathematics

Mean of a distribution; also a measure (∫f dμ) in advanced probability.

Physics

Coefficient of friction, magnetic moment, chemical potential, reduced mass.

Biology

Mutation rate per site per generation; growth rate in microbial kinetics.

AI / ML

Mean of a Gaussian (e.g. a VAE encoder outputs μ and σ); running mean in normalisation layers.

In a research paper

Layer normalisation (Ba et al. 2016) and batch normalisation, used inside transformers.

\hat{x} = \frac{x - \mu}{\sqrt{\sigma^2 + \epsilon}}

Shift the numbers so they are centred on zero, then rescale so their spread is about 1.

Common misreadings

Confusing the population mean μ with a sample average (usually written x̄).
Reading µ in "µm" as a variable rather than the micro- prefix.

Connected symbols

\sigma

Sigma (lowercase)

\mathbb{E}

Expectation (expected value)

\beta

Beta

Where it appears on this site

§ 4. Probability, Entropy, and Information § 8. The Scientific Skeptic’s Toolkit