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Standard deviation calculator

Paste your values to calculate standard deviation and a complete descriptive statistics summary.

Sample standard deviation s: —

Fill in the fields above — the result is computed on this page.

Observations
—
Mean
—
Median
—
Mode
—
Sample variance s²
—
Population standard deviation σ
—
Population variance σ²
—
Minimum
—
Q1
—
Q3
—
Maximum
—
Range
—
IQR
—

What do these numbers mean?
  • A larger standard deviation means greater spread in the original unit.
  • Standard deviation has the data unit; variance has the squared unit.

The measure is sensitive to outliers. The sample or population formula must match what the data represents.

How do I use this page?
  1. Paste at least two values.
  2. Use s for a sample or σ for a population.
  3. Check quartiles and range before interpreting spread.

What this page does not do: The measure is sensitive to outliers. The sample or population formula must match what the data represents.

Further reading

Theory — what is standard deviation?

Standard deviation measures the typical distance of values in a dataset from their mean. For a sample, the sum of squared deviations is divided by n−1, while for a full population it is divided by n, giving slightly different results for the same numbers. The same data also yields the five-number summary, quartiles, the interquartile range, the range and the mode. The n−1 method is used when the data is a sample meant to estimate the variability of a larger population.

Frequently asked questions

When should I divide by n−1?
Use n−1 when the values are a sample used to estimate the variability of a larger population.
Is a small standard deviation always good?
No. Its meaning depends on the unit, scale and purpose of the analysis.

See also

← All calculators

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