Standard Deviation Calculator
Calculate standard deviation and variance
Calculator
How to Use
Calculate standard deviation and variance
Enter data
Input your list of numbers
Choose type
Select population or sample
View results
See mean, variance, and standard deviation
Interpret
Understand what the SD means for your data
Standard Deviation Formula
Sample: s = √[Σ(x-x̄)²/(n-1)] Population: σ = √[Σ(x-μ)²/n]
Variance is the average squared deviation from mean. Standard deviation is the square root of variance.
Frequently Asked Questions
Standard deviation measures how spread out data is from the mean. Low SD = data clustered near mean. High SD = data spread widely. For test scores with mean 75 and SD 10: most scores fall between 65-85 (one SD from mean).
Find mean, subtract mean from each value, square differences, average the squares (variance), take square root. Formula: σ = √(Σ(x-μ)²/n) for population, s = √(Σ(x-x̄)²/(n-1)) for sample.
Population SD (σ) divides by n, used when data represents entire population. Sample SD (s) divides by n-1, used when data is a sample (most common). n-1 corrects for bias in estimating population SD from a sample.
For normal distributions: 68% of data falls within 1 SD of mean, 95% within 2 SD, 99.7% within 3 SD. Example: IQ has mean 100, SD 15. 68% score 85-115, 95% score 70-130, 99.7% score 55-145.