Math & Calculators
Standard Deviation Calculator
Calculate standard deviation, variance, mean, and other statistics for a data set.
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Separate numbers with commas
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What is Standard Deviation Calculator?
Standard deviation measures how spread out numbers are from their average. A low standard deviation means data points cluster near the mean, while a high one indicates wide variation. It's a fundamental concept in statistics, quality control, and data analysis.
How to Use
- Enter your data set as comma-separated numbers
- Choose between population and sample standard deviation
- View the mean, variance, and standard deviation results
- Review the step-by-step calculation breakdown
Formula
SD = sqrt( Sum of (xi - mean)^2 / N ) for population, or / (N-1) for sample
Frequently Asked Questions
- When should I use population vs. sample standard deviation?
- Use population when you have data for the entire group. Use sample (divides by N-1) when your data is a subset representing a larger population.
- What does a standard deviation of 0 mean?
- It means every value in your data set is identical -- there is zero variation.
- How does standard deviation relate to the bell curve?
- In a normal distribution, about 68% of data falls within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs.