Standard Deviation Calculator
Enter numeric values to see the mean along with population and sample standard deviations using the classic formulas.
Count
6
Mean
19.5000
Population SD
5.1235
Sample SD
5.6125
Variance Details
Population variance
26.2500
Sample variance
31.5000
Population std. dev.
5.1235
Sample std. dev.
5.6125
Mean
19.50
How to Use This Calculator
- Enter numeric data using spaces or commas to separate values.
- Review the mean, variance, and standard deviation results presented in the cards.
- Use population statistics when you have the full dataset; use sample statistics when working with a subset.
- Pair standard deviation with range, IQR, or skewness for a more complete variability profile.
Formulas
Population variance = Σ(x − μ)² / N
Sample variance = Σ(x − μ)² / (n − 1)
Population standard deviation = √(population variance)
Sample standard deviation = √(sample variance)
Sample mean μ = Σx / n
The sample formulas use (n − 1) to provide an unbiased estimator of population variance (Bessel's correction).
Frequently Asked Questions
When should I use population vs. sample SD?
Use population statistics when your data contain every observation of interest. Use sample statistics when the dataset represents a sample from a larger population.
Can standard deviation be zero?
Yes. Standard deviation is zero when all values are identical.
Do negative numbers affect standard deviation?
No. Squared deviations remove the sign, so negative values contribute just like positive ones.
Is standard deviation sensitive to outliers?
Yes. Extreme values increase the variance and standard deviation noticeably. Consider robust measures like IQR when outliers are present.