Standard Deviation Calculator
Calculate standard deviation
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out data values are from the mean. A low SD means data points cluster near the average; a high SD means they are spread widely. The formula is: σ = √(Σ(x-μ)²/N) for population, or s = √(Σ(x-x̄)²/(n-1)) for sample.
What is the difference between population and sample standard deviation?
Population SD (σ) divides by N (total count). Sample SD (s) divides by n-1 (Bessel's correction) to account for estimation bias. Use population SD when you have all data points; use sample SD when working with a subset.
What does the 68-95-99.7 rule mean?
For normally distributed data: 68% of values fall within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. If mean = 100 and SD = 15: 68% of values are between 85-115, 95% between 70-130.
How is standard deviation used in finance?
In investing, SD measures volatility. A stock with 20% annual SD is more volatile than one with 10%. Higher SD means higher risk but potentially higher returns. The Sharpe ratio uses SD to measure risk-adjusted returns.
What is variance and how does it relate to standard deviation?
Variance is the square of standard deviation: Variance = SD². If SD = 5, variance = 25. Variance is useful in statistical calculations, but SD is more interpretable because it is in the same units as the data.