Standard Deviation Calculator
Calculate your Spread measure in seconds with the free Standard Deviation Calculator. No registration needed.
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What is a Standard Deviation Calculator?
A standard deviation calculator measures how spread out the numbers in a data set are from the mean. It computes both sample and population standard deviation, helping you understand the variability in your data.
How to calculate standard deviation manually (the formula)
First, find the mean. Then for each value, subtract the mean and square the result. Sum all squared differences and divide by n (population) or n−1 (sample). Finally, take the square root. Formula: σ = √(Σ(xi − μ)² / N).
Example calculation
For 4, 8, 15, 16, 23, 42: mean = 18. Deviations: (−14)² + (−10)² + (−3)² + (−2)² + 5² + 24² = 196 + 100 + 9 + 4 + 25 + 576 = 910. Population SD = √(910 / 6) ≈ 12.32.
Common mistakes
- Using the wrong denominator — Use n for population, n−1 for sample. Mixing them gives incorrect results.
- Forgetting to square the deviations — Always square each difference before summing, or the result will be zero.
- Confusing variance with standard deviation — Variance is the square of the standard deviation. Standard deviation is in the original units; variance is in squared units.
Frequently asked questions
What is standard deviation?
A measure of how spread out numbers are from the mean.
What is the difference between sample and population standard deviation?
Population uses N; sample uses N−1 to correct for bias.
How is standard deviation calculated?
Find the mean, square each deviation, average them, and take the square root.
What does a high standard deviation mean?
Data points are spread widely around the mean.
What is the symbol for standard deviation?
σ for population, s for sample.
Can standard deviation be negative?
No, it is always zero or positive.