Standard Deviation Calculator
Sample or population • Raw list or value:count
Inputs
Separators: comma, space, newline, semicolon. Frequency format: value:count, where count must be a positive integer.
Turn this off to calculate population standard deviation using n.
Large datasets are previewed in compressed form.
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Results
Std deviation
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Variance
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Mean
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Count (n)
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Min / Max
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Range
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Use this Standard Deviation Calculator to calculate sample or population standard deviation, variance, and mean from a numeric dataset.
Calculation Method
Sample standard deviation:
s = √[Σ(x − x̄)² ÷ (n − 1)]
Population standard deviation:
σ = √[Σ(x − μ)² ÷ N]
Standard deviation is the square root of variance.
Example
For:
2, 4, 4, 4, 5, 5, 7, 9
The mean is 5 and the sum of squared deviations is 32.
Population SD = √(32 ÷ 8) = 2
Sample SD = √(32 ÷ 7) ≈ 2.14
Important Note
Use sample standard deviation when the data represent a sample from a larger population. Standard deviation is sensitive to extreme values and does not by itself show that data follow a normal distribution.