Standard Deviation Calculator
Calculate mean, variance, and standard deviation (population and sample) from a data set.
By Konstantin Iakovlev · Updated April 2026 · Source: Khan Academy
Population SD
4.8990
Sample SD
5.2372
Mean
18.0000
Statistics
| Count (n) | 8 |
| Sum | 144.00 |
| Mean | 18.0000 |
| Population Variance (σ²) | 24.0000 |
| Population Std Dev (σ) | 4.8990 |
| Sample Variance (s²) | 27.4286 |
| Sample Std Dev (s) | 5.2372 |
| Minimum | 10.00 |
| Maximum | 23.00 |
| Range | 13.00 |
Sorted Data
10.00, 12.00, 16.00, 16.00, 21.00, 23.00, 23.00, 23.00
Use the Standard Deviation Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.
Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.
How It Works
Feed in a data set and this calculator returns its mean, variance, and both the population and sample standard deviation in a single pass. Those figures describe how tightly or loosely values cluster, which is why they turn up wherever spread matters—gauging 2026 stock market volatility, tracking 2026 climate temperature swings, or checking whether a manufacturing line stays within tolerance.
Calculation starts with the mean, the simple average of your values. Variance comes next, averaging the squared distance of each point from that mean to capture overall spread. Taking the square root of the variance yields the standard deviation, expressed in the same units as your data; the population version divides by N, while the sample version divides by N-1 to correct for the bias that creeps in when you estimate from a subset.
Choosing the right version is not optional—applying the population formula to sample data, or vice versa, skews your conclusions, and the distortion grows sharper as data sets shrink. Confirm that every entry is numerical and that nothing was mistyped. One frequent slip is treating variance and standard deviation as interchangeable; only the standard deviation carries the original units, which is what makes it directly interpretable.
Example: Analyzing 2026 Quarterly Sales Performance
- 1 Imagine a small business recorded its quarterly sales (in thousands of USD) for 2026 as follows: Q1: $120, Q2: $135, Q3: $110, Q4: $145. Enter these values into the calculator.
- 2 The calculator will first find the mean: (120+135+110+145)/4 = $127.5 thousand. Then, it calculates the squared differences from the mean and sums them. For population variance, it divides by 4; for sample variance, it divides by 3. Finally, it takes the square root for the standard deviation.
- 3 The calculator will output: Mean = $127.5 thousand. Population Variance = 171.875. Population Standard Deviation = $13.11. Sample Variance = 229.167. Sample Standard Deviation = $15.14.
- 4 This means that, on average, the business's 2026 quarterly sales deviated by approximately $13,110 from the mean sales of $127,500 (assuming this is the entire 'population' of their 2026 sales). If these four quarters were just a sample of a larger sales trend, the sample standard deviation of $15,140 would be a better estimate for the typical deviation.
Source: Khan Academy · Last updated: April 2026
Frequently Asked Questions
What is the difference between population and sample standard deviation?
What does standard deviation tell you?
What is considered a high standard deviation?
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