DocomintStandardabweichungsrechner
Berechne Stichproben- und Grundgesamtheits-Standardabweichung sowie Varianz für eine Zahlenmenge.
What is a Standardabweichungsrechner?
Standard deviation measures how spread out a data set is around its mean — a small value means the numbers cluster tightly, a large one means they're scattered. This computes both the sample formula (dividing by n-1, the one used when your numbers are a subset of a bigger population — the common case for survey data or a class's test scores) and the population formula (dividing by n, for when your list is the entire population you care about), since which one is "correct" depends on which situation you're in.
How to use the Standardabweichungsrechner
- Paste a list of numbers, separated by commas or one per line
- Press Calculate
- Both sample and population standard deviation appear instantly, computed on your device
Formula
Population: σ = √(Σ(x − mean)² ÷ n) | Sample: s = √(Σ(x − mean)² ÷ (n − 1))
Both formulas measure spread around the mean; the sample version divides by n−1 instead of n, which corrects for the fact that a sample tends to slightly understate the true population's variability.
Example
Seven data points — 4, 8, 6, 5, 3, 9, 7 — have a mean of 6 and a sample standard deviation of about 2.16, meaning most values sit within roughly 2 points of the mean.
Common mistakes
- Using the population formula (÷n) when the data is actually a sample meant to estimate a larger group — that understates the true spread.
- Reporting variance when standard deviation was asked for — variance is standard deviation squared, in squared units that aren't directly comparable to the original data.
- Running this on a single number and expecting a sample standard deviation — it's mathematically undefined with fewer than 2 values.
Frequently asked questions
What's the difference between population and sample standard deviation?
Population standard deviation (dividing by n) is used when your data is the entire group you care about. Sample standard deviation (dividing by n−1) is used when your data is a subset used to estimate a larger population — the more common case for survey or experimental data, and why it's shown first here.
What does a high standard deviation mean?
It means the values are spread widely around the mean rather than clustered close to it. A low standard deviation means the values are consistent and close together; a high one means more variability or volatility in the data set.
What units is the result in?
The same units as your original data — standard deviation of a list of dollar amounts is in dollars, not squared dollars (that's variance).
Can I paste data copied directly from a spreadsheet column?
Yes — a newline-separated column pastes in cleanly, the same as a comma-separated list.
Is my numbers uploaded anywhere?
No — Standardabweichungsrechner runs entirely in your browser using JavaScript/WebAssembly. Your numbers is never sent to a server.