Statistics & Mean / Median / Mode
Compute mean, median, standard deviation, and variance for data sets.
Last reviewed by the myCalculator Editorial Team
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Formula & How Statistics & Mean / Median / Mode Works
The mean is the sum of the numbers divided by how many there are, and the standard deviation measures how far the numbers typically sit from the mean. For 10, 20 and 30 the mean is 20, the deviations are −10, 0 and +10, their squares are 100, 0 and 100 (total 200), and the population variance is 200 ÷ 3 = 66.7, giving a standard deviation of 8.2. For a sample drawn from a larger group, divide by n − 1 instead: 200 ÷ 2 = 100, a standard deviation of 10. Use the population version when your numbers are the complete set and the sample version when they are a subset. A small standard deviation means the values cluster tightly around the mean.
- Enter Enter Numbers (comma or space separated): Input your target parameter value.
- Apply Formula: Calculate using
Mean = Σx / N, StdDev = √(Σ(x - μ)² / N). - Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)
What is standard deviation?
A measure of how spread out numbers are from their average value.
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Authoritative Standards & Verified Reference Citations
Calculations and mathematical logic on this page are grounded in published statutory rules, regulatory standards, and official government data published by the following bodies:
Open government data, scientific datums, and public sector mathematical reference datasets.
Australia's national authority on physical, chemical, and biological metric measurement standards.
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