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Standard Deviation Calculator

Calculate sample and population standard deviation, variance, and mean for any dataset.

Result:
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Contents

How Standard Deviation Calculator Works & Mathematical Formula

Calculate sample and population standard deviation, variance, and mean for any dataset. Our online engine computes high-precision results in real-time right in your browser without transmitting your personal information over external servers.

Standard Mathematical Formula:
$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} \quad \text{(Sample)}, \quad \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \quad \text{(Population)}$$

Step-by-Step Calculation Example

For dataset [10, 20, 30, 40, 50]: Mean = 30. Sample Standard Deviation (s) = 15.8114. Sample Variance (s²) = 250. Population Standard Deviation (σ) = 14.1421.

Frequently Asked Questions

What is the difference between sample and population standard deviation?

Use sample standard deviation (dividing by n - 1) when your data represents a sample of a larger group. Use population standard deviation (dividing by N) when your data contains every member of the group.

What does a low vs high standard deviation mean?

A low standard deviation means data points are clustered closely around the mean, while a high standard deviation indicates data is spread out over a wider range of values.