Standard Deviation Calculator
Calculate mean, variance, standard deviation, and coefficient of variation for any dataset. Population and sample modes.
6 numbers detected
Mean (Average)
18
Median
15.5
Std Deviation
13.4907
Variance
182
Min
4
Max
42
Range
38
CV (%)
74.95%
About the Standard Deviation Calculator
Standard deviation measures how spread out your data is around the mean. A low standard deviation means values cluster tightly around the average; a high one means they are widely scattered. In finance, standard deviation measures portfolio volatility - a fund with 12% average return and 8% std dev is less predictable than one with 12% return and 3% std dev. In quality control, it determines whether a manufacturing process is consistent.
Standard Deviation Formula
Population SD: σ = sqrt(Σ(x - μ)² / N) · Sample SD: s = sqrt(Σ(x - x̄)² / (N-1))
μ or x̄ = mean · N = total count · Use sample SD (N-1) when working with a sample, not the full population · Variance = SD² · 68-95-99.7 rule: 68% of data falls within 1 SD of mean, 95% within 2 SD, 99.7% within 3 SD
Worked Example
Monthly returns of a mutual fund over 6 months: 2%, 5%, -1%, 8%, 3%, 4%
Deviations squared: 2.25, 2.25, 20.25, 20.25, 0.25, 0.25 · Variance = 45.5/5 = 9.1 · Sample SD ≈ 3.02% · 68% of months should fall between 0.48% and 6.52%
Tips & Insights
- 1
Use sample standard deviation (N-1 denominator) for any dataset that is a sample from a larger population.
- 2
Coefficient of variation = SD / Mean expresses variability relative to the average - useful for comparing datasets with different units.
- 3
In finance, annualized volatility = monthly SD × sqrt(12). A monthly SD of 3% = annual volatility of 10.4%.
Why this matters for you
Standard deviation is the fundamental measure of risk in finance, quality control, and scientific measurement. When a mutual fund advertises '15% CAGR', the standard deviation tells you how much that figure varies year to year. Two funds with identical returns but different standard deviations offer very different investor experiences - and the risk-adjusted comparison (Sharpe ratio) uses standard deviation as its risk measure.
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