Standard Deviation Calculator
Quantify the dispersion and spread of dataset observations relative to their arithmetic mean. Computes both Bessel-corrected sample standard deviation (s) and population standard deviation (σ).
Enter values separated by commas, spaces, or tabs
Choose sample if evaluating a subset; population if whole universe
Square root of variance in native units
How to Use This Calculator
- Enter or paste numbers separated by commas or spaces.
- Select Sample (n-1) or Population (N) mode.
- View the standard deviation, variance, and mean instantly.
Formula & Calculation Methodology
Standard deviation measures the average distance of observations from their mean. Dividing by n-1 for samples eliminates downward bias when estimating population parameters.
Worked Example
Evaluating sample: 10, 12, 23, 23, 16, 23, 21, 16
Evaluating population: 2, 4, 4, 4, 5, 5, 7, 9
Frequently Asked Questions
When should I choose Sample versus Population?↓
Choose Sample if your data represents a portion or survey of a wider group. Choose Population only when you possess all existing measurements in existence.
Why does Bessel correction divide by n - 1?↓
Dividing by n underestimates population variance because sample points are naturally closer to the sample mean than to the true population mean. Using n - 1 corrects this bias.
Can standard deviation ever be negative?↓
No. Because it is calculated by taking the principal square root of non-negative squared deviations, standard deviation is always ≥ 0.
What is a limitation of standard deviation?↓
Like the mean, standard deviation is sensitive to extreme outliers, as squaring deviations magnifies large discrepancies.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.