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Standard Deviation Calculator

Calculate key statistical dispersion metrics including Sample Standard Deviation (s), Population Standard Deviation (σ), Sample Variance (s²), Population Variance (σ²), Mean (μ), and Total Sample Size (N) for any numeric data set.

Interactive Standard Deviation Calculator

Math

Statistical Metrics

Sample Std Dev (s): 15.8114
Mean (μ): 30.00
Variance (s²): 250.00
Count (N): 5

How to Use the Standard Deviation Calculator

  • Enter a series of numbers separated by commas, spaces, or line breaks into the input box.
  • The tool instantly parses your dataset to compute mean, sum of squared differences, sample variance, and sample standard deviation.
  • Use the results to evaluate statistical spread, probability distribution, and data variance.

Formula & Calculation Methodology

Sample Std Dev (s) = √[ Σ(x - x̄)² / (n - 1) ] | Population Std Dev (σ) = √[ Σ(x - μ)² / N ]

Our mathematical algorithms adhere to standard scientific and financial guidelines to deliver maximum accuracy.

Frequently Asked Questions

What is the difference between sample and population standard deviation?

Sample standard deviation divides the sum of squared differences by (n - 1) using Bessel's correction to account for sample estimation bias, whereas population standard deviation divides by N because all data points in the true population are known.

What does a high standard deviation mean?

A high standard deviation indicates that the data points are spread out widely over a large range of values away from the mean, whereas a low standard deviation means data points cluster closely near the average.

How do you calculate variance from standard deviation?

Variance is simply the square of the standard deviation (Variance = s² or σ²).

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