Standard Deviation Calculator
Calculate mean, variance, and standard deviation (population and sample) from a data set.
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
Our Standard Deviation Calculator helps you quickly determine the mean, variance, and both population and sample standard deviation for any given data set. This is crucial for understanding data dispersion, whether you're analyzing 2026 stock market volatility, predicting 2026 climate temperature variations, or assessing the consistency of manufacturing processes.
The calculator first computes the mean (average) of your data. Variance then measures the average of the squared differences from the mean, providing a sense of spread. Finally, the standard deviation, the square root of the variance, quantifies the typical deviation of data points from the mean, with separate formulas applied for population (dividing by N) and sample (dividing by N-1) standard deviations to ensure unbiased estimation.
Always distinguish between population and sample standard deviation; using the wrong one can lead to inaccurate conclusions, especially with smaller datasets. Ensure your data is numerical and that you've correctly entered all values. A common mistake is to confuse standard deviation with variance, remember standard deviation is in the same units as your original data.
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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