Standard Deviation Calculator
Calculate the mean, variance, and standard deviation of a data set for both population and sample datasets.
The standard deviation of the dataset is 3.8914.
For your 7-point dataset, the mean is 7.1429. The sum of squared deviations from the mean is 90.8571. Dividing by n - 1 yields a variance of 15.1429. Taking the square root gives a standard deviation of 3.8914.
How to Use the Standard Deviation Calculator
Calculate the standard deviation of any data set with our free statistics calculator. Enter your numbers as a comma-separated list to instantly compute the mean, variance, and both population and sample standard deviations. View step-by-step working to understand exactly how the result is derived.
- Data Values (comma-separated): Bounded parameter in the mathematical model.
- Data Type: Bounded parameter in the mathematical model.
What Is Standard Deviation? Variance & Data Spread
Understand standard deviation, variance, and the 68-95-99.7 rule — the primary statistical measure of data spread used in finance, science, and quality control.
Read Full Guide →Normal Distribution: Bell Curve & Standard Scores
Discover why the bell curve appears everywhere in nature, how the 68-95-99.7 rule works, and how to use z-scores to interpret any normally distributed dataset.
Read Full Guide →What is the difference between population and sample standard deviation?
Population standard deviation (σ) is used when you have data for an entire population. It divides the sum of squared deviations by N. Sample standard deviation (s) is used when your data represents a subset of a larger population. It divides by N-1 (Bessel's correction) to account for sampling bias and produce an unbiased estimate.
What does a high standard deviation mean?
A high standard deviation means the data points are spread out widely around the mean. A low standard deviation means the data points are clustered closely together. In finance, high standard deviation represents higher volatility. In manufacturing, low standard deviation is the hallmark of consistent quality.
What is the formula for standard deviation?
For a sample: s = √(Σ(xᵢ - x̄)² / (n-1)), where x̄ is the sample mean and n is the number of values. For a population: σ = √(Σ(xᵢ - μ)² / N), where μ is the population mean and N is the total number of values.
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