The population standard deviation is written σ, the lowercase Greek letter sigma. The sample standard deviation is written s. Choosing the wrong one is the most common notation error in introductory statistics, and this page explains the system that makes the choice obvious.
The complete notation table
| Symbol | Say it | Means | Population or sample |
|---|---|---|---|
| σ | sigma | Standard deviation | Population |
| s | ess | Standard deviation | Sample |
| σ² | sigma squared | Variance | Population |
| s² | ess squared | Variance | Sample |
| μ | mu | Mean | Population |
| x̄ | x-bar | Mean | Sample |
| N | big en | Number of values | Population |
| n | little en | Number of values | Sample |
| Σ | capital sigma | "Add all of these up" | Either |
| σx̄ / SE | sigma x-bar | Standard error of the mean | Either |
| σp / sp | sigma pooled | Pooled standard deviation | Either |
| z | zee / zed | Z-score, in standard deviations | Either |
| CV / %RSD | — | Spread relative to the mean | Either |
The rule behind the whole system
Statistics uses a consistent convention that makes almost all of this table predictable:
- Greek letters describe populations. σ, μ, ρ, β. These are parameters — fixed, real, and usually unknowable.
- Roman letters describe samples. s, x̄, r, b. These are statistics — computed from data you actually have, and different for every sample you might draw.
So the question "σ or s?" is really the question "is this number describing a whole population, or a sample drawn from one?" — the same question that decides which denominator to use in the formula. Answer it once and the notation follows.
σ and Σ are not the same symbol
Both are called sigma and they appear in the same formula, which causes real confusion:
σ = √[ Σ(x − μ)² / N ]
Lowercase σ is a quantity — the standard deviation itself, the thing being defined. Capital Σ is an instruction — an operator that says "sum the following over every value". One is a noun, the other is a verb.
How to type each symbol
| Symbol | Windows | Mac | LaTeX | HTML | Unicode |
|---|---|---|---|---|---|
| σ | Alt+229 | Char viewer | \sigma | σ | U+03C3 |
| Σ | Alt+228 | Option+w (∑) | \Sigma | Σ | U+03A3 |
| μ | Alt+230 | Option+m | \mu | μ | U+03BC |
| x̄ | x then Alt+0772 | x + combining macron | \bar{x} | x̄ | U+0304 |
In Word, typing the Unicode hex code and pressing Alt+X converts it in
place — so 03C3 then Alt+X gives σ. On a Mac,
Ctrl+Cmd+Space opens the character viewer where you can
search by name.
Note that x̄ is not a single character: it is the letter x followed by U+0304, the combining macron. That is why it sometimes renders badly in fonts that lack proper combining-mark support, and why copying it out of a PDF often loses the bar.
Notation you may also meet
- σ̂ ("sigma-hat") — an estimate of σ. Some texts write σ̂ where others write s. The hat always means "estimated from data".
- SD — plain text for standard deviation, common in journals: "mean 24.1 (SD 3.2)".
- SEM — standard error of the mean. Frequently confused with SD in published figures; check which one an error bar represents, because SEM is always the smaller and more flattering of the two.
- sx and σx — the standard deviation of a variable named x, used when several variables are in play.
- σn and σn−1 — the labels Casio and Sharp calculators print for the population and sample standard deviations. TI calculators use σx and Sx for the same pair.
Related calculators
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The formula explained
Where each of these symbols appears, and what it does there.
-
Sample vs population
The distinction that σ and s exist to mark.
-
Standard deviation calculator
Compute σ or s from your own numbers.
-
Standard error
The σx̄ in the table above, calculated.
Common questions
What is the symbol for standard deviation?
It depends on which standard deviation you mean. The population standard deviation is the lowercase Greek sigma, σ. The sample standard deviation is a plain italic s. Using σ for a sample statistic is the single most common notation mistake in introductory statistics.
What is the difference between σ and s?
σ is a parameter — a fixed, usually unknown property of a whole population. s is a statistic — a number computed from a sample, which varies from sample to sample and is used to estimate σ.
The convention runs throughout statistics: Greek letters for the truth you cannot see, Roman letters for the estimates you can compute. μ and x̄ follow the same pattern.
How do I type the σ symbol?
Windows: hold Alt and type 229 on the numeric keypad, or use
Win+. and search "sigma".
Mac: Option+w gives ∑ (summation); for σ use
Ctrl+Cmd+Space and search "sigma".
Word: type 03C3 then press Alt+X.
LaTeX: \sigma for σ, \Sigma for Σ.
HTML: σ and Σ.
What does the Σ symbol mean?
Capital sigma, Σ, is the summation operator — it means "add up everything that follows".
It is a different symbol from lowercase σ despite sharing a name. In
Σ(x − x̄)² it instructs you to compute (x − x̄)² for every value and total the
results.
What is σ² and what is σx̄?
σ² is the variance — the standard deviation squared. σx̄ (sometimes written σ_M or SE) is the standard error of the mean, the standard deviation of the sampling distribution of the mean, equal to σ/√n.