Standard Deviation Calculator

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Population standard deviation (divide by n instead of n-1)

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What is Standard Deviation?

Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that values tend to be close to the mean, while a high standard deviation indicates that values are spread out over a wider range.

Standard Deviation Formulas

Sample Standard Deviation

s = √[Σ(x - x̄)² / (n - 1)]

Use this when your data represents a sample from a larger population.

Population Standard Deviation

σ = √[Σ(x - μ)² / N]

Use this when your data represents the entire population.

Understanding the Results

• 68% of data falls within 1 standard deviation of the mean
• 95% of data falls within 2 standard deviations
• 99.7% of data falls within 3 standard deviations

This is known as the Empirical Rule or 68-95-99.7 Rule for normally distributed data.

Sample vs. Population

Choose Sample when:

• Your data is a subset of a larger group
• You want to estimate the population variability
• Most practical applications

Choose Population when:

• You have data for the entire group
• You’re calculating for a complete, finite dataset

Related Tools

• Mean Calculator - Calculate the average
• Z-Score Calculator - Standardize your values
• Histogram Generator - Visualize your data distribution