Statistics

Standard Deviation Calculator

Calculate standard deviation, variance, and other dispersion statistics for sample or population data

Use when data is a subset of a larger group (divides by n-1)

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Calculate Standard Deviation Instantly

Standard deviation measures how spread out your data is from the mean. Our calculator computes both sample and population standard deviation, along with variance and coefficient of variation. Essential for statistics students, researchers, and data analysts.

What is Standard Deviation?

Standard deviation (σ for population, s for sample) measures the average distance of data points from the mean. A low standard deviation means data points cluster close to the mean, while a high standard deviation indicates data is spread out. Variance is simply the standard deviation squared.

Standard Deviation Formula

s = √[Σ(xᵢ - x̄)² / (n-1)]

How to Calculate Standard Deviation

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Standard Deviation Applications

Quality Control

Monitor manufacturing consistency and detect variations.

Finance

Measure investment risk and portfolio volatility.

Research

Analyze experimental data and report variability.

Education

Understand test score distributions and grading curves.

Frequently Asked Questions

Use population SD when you have data for the entire group you're studying (like test scores for an entire class). Use sample SD when you're estimating based on a subset (like surveying 100 people from a city). When in doubt, use sample SD—it's more conservative.