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- Enter your numbers separated by commas, spaces or line breaks.
- Choose sample (most common) or population.
- Review the deviation table to see how each value contributes.
Formel
Standard deviation measures how spread out values are around the mean. The sample formula divides by n − 1 (Bessel's correction) to give an unbiased estimate of the population variance.
Population: σ = √( Σ(x − μ)² / N )
Sample: s = √( Σ(x − x̄)² / (n − 1) )
Example
- Data: 2, 4, 4, 4, 5, 5, 7, 9; mean = 5.
- Squared deviations sum to 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32.
- Population σ = √(32/8) = 2; sample s = √(32/7) ≈ 2.138.
Häufige Fragen
What does a large standard deviation mean?
Values are spread widely around the mean. A small standard deviation means values cluster closely around it.
What is the 68–95–99.7 rule?
For roughly normal data, about 68% of values fall within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3.
Variance vs. standard deviation?
Variance is the average squared deviation; standard deviation is its square root, which has the same units as the data and is easier to interpret.