Standard Deviation Calculator
Calculate mean, median, mode, SD, variance and range from any dataset
Data Set
Enter numbers separated by commas, spaces, or new lines. Minimum 2 values required.
Quick Formulas
Mean = Σx / n
Variance (pop) = Σ(x−μ)² / n
Variance (sample) = Σ(x−x̄)² / (n−1)
SD = √Variance
Mean (Average)
—
Median: — · Mode: —
Std Dev (Population)—
Std Dev (Sample)—
Variance (Sample)—
Range (Max − Min)—
Count (n)—
Min / Max— / —
Sum—
Population vs Sample Standard Deviation
When your data represents the entire population, divide by n (population SD). When your data is a sample from a larger population — which is almost always the case in practice — divide by n−1 (sample SD). This correction (Bessel's correction) reduces bias in estimating the population variance from sample data.
Most statistics courses and calculators use sample SD (n−1) by default. Excel's STDEV() uses sample SD; STDEVP() uses population SD.
lightbulb Interpreting SD
1Small SD → data clustered near mean
2Large SD → data is spread out
368% of data lies within 1 SD of mean (normal dist)
✓ 95% within 2 SD; 99.7% within 3 SD