Standard Deviation Calculator
Calculate population or sample standard deviation and variance. Free online Standard Deviation Calculator for statistics — instant, accurate results, no signup.
Derivation
- ├── 01Given
n = 8, data = 2, 4, 4, 4, 5, 5, 7, 9 - ├── 02Mean x̄
(2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 5.0000 - ├── 03Formula
s = √(Σ(xᵢ − x̄)² / (n − 1)) (sample, Bessel correction) - ├── 04Squared deviations
(2 − 5.00)² = 9.0000; (4 − 5.00)² = 1.0000; (4 − 5.00)² = 1.0000; (4 − 5.00)² = 1.0000; (5 − 5.00)² = 0.0000; (5 − 5.00)² = 0.0000; (7 − 5.00)² = 4.0000; (9 − 5.00)² = 16.0000 - ├── 05Σ(xᵢ − x̄)²
32.000000 - ├── 06Variance
32.000000 / 7 = 4.571429 - └── 07Sample SD (s)√4.571429 = 2.138090
The arithmetic mean goes back to Babylon; the median was formalised by Gustav Fechner (1874); "mode" was coined by Karl Pearson in 1895.
Understanding the Standard Deviation Calculator
The Standard Deviation Calculator helps you compute calculate population or sample standard deviation and variance.. It runs entirely in your browser with no sign-up required.
Statistics is how we make sense of noisy real-world data. Whether you’re analysing survey results, sports scores, or business metrics, a statistics calculator gives you the exact formula-based answer so you can focus on the interpretation. The Standard Deviation Calculator sits in that toolkit — it calculate population or sample standard deviation and variance. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.
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