Standard Deviation Calculator
Calculate Mean, Variance, Sample Standard Deviation, and Population Standard Deviation
Calculator
Enter a list of numbers separated by commas, spaces, or line breaks.
About the Standard Deviation Calculator
The Standard Deviation Calculator helps you quickly determine the spread or variability of a dataset for statistics, engineering, science, and data analysis. It computes both population standard deviation and sample standard deviation to provide a full understanding of how data points differ from the mean.
What You Can Calculate
- Mean (Average): The central value around which the dataset varies.
- Variance: Measures how far data points spread out from the mean.
- Sample Standard Deviation (s): Used when working with a subset of a population.
- Population Standard Deviation (σ): Used when analyzing an entire population.
Formulas Used in the Calculator
The calculator uses standard mathematical formulas for both population and sample statistics:
- Mean: μ = (Σx) / N
- Population Variance: σ² = Σ(x − μ)² / N
- Sample Variance: s² = Σ(x − x̄)² / (n − 1)
- Standard Deviation: σ = √σ² or s = √s²
How to Use the Calculator
- Enter your dataset as comma-separated numbers.
- Select whether to compute sample or population standard deviation.
- The calculator instantly displays the mean, variance, and standard deviation.
Applications of Standard Deviation
Standard deviation is essential for quality control, engineering analysis, risk assessment, scientific research, and statistical modeling. It helps quantify data variability, detect outliers, and compare the consistency of different datasets.