Calculate stable population and sample statistics, inspect observed-data dispersion and review centered deviations without assuming normality.
01 / PURPOSE-SPECIFIC INPUTS
02 / RESULT & INTERACTIVE INSPECTION
These are descriptive statistics. A sample SD is not a standard error, confidence interval or proof of normally distributed data. Numeric display precision is separate from measurement accuracy.
Observation 1: 2; centered deviation -3; squared deviation 9. Frequency of this exact numeric value: 1.
| Observation | Value | Deviation from computed center | Squared deviation |
|---|---|---|---|
| 1 | 2 | -3 | 9 |
| 2 | 4 | -1 | 1 |
| 3 | 4 | -1 | 1 |
| 4 | 4 | -1 | 1 |
| 5 | 5 | 0 | 0 |
| 6 | 5 | 0 | 0 |
| 7 | 7 | 2 | 4 |
| 8 | 9 | 4 | 16 |
Enter your values locally; no inputs are uploaded.
Check validation feedback before reviewing the browser-generated result.
Review the explanation, copy supported outputs or reset the workspace.
Population variance divides the sum of squared deviations by N. Its square root is population SD. A single constant observation has population variance and SD zero.
Calculate stable population and sample statistics, inspect observed-data dispersion and review centered deviations without assuming normality. Inspect actual values and worked assumptions through accessible interactive controls.
Standard Deviation Calculator calculations run locally in browser memory. Expressions, measurements, schedules and datasets are not sent to an external calculation-processing API or saved as a personal profile. Ordinary website requests may still be logged. Clipboard access occurs only when you choose Copy Result.
Population variance divides the sum of squared deviations by N. Its square root is population SD. A single constant observation has population variance and SD zero.
Sample variance divides by N−1, so it is undefined when N is one. Sample mode rejects a one-observation dataset, while population mode labels sample statistics undefined.
Mean is 5, population variance 4 and population SD 2. Sample variance is 32/7, approximately 4.57142857, and sample SD is approximately 2.13809.
A shifted-origin Welford update accumulates centered squared differences rather than subtracting two large raw sums of squares. Sum uses compensated addition; finite input parsing still cannot recover digits beyond machine precision.
No. It plots actual observed values with duplicate stacks and descriptive mean/SD markers. It does not infer a bell curve, confidence interval, standard error or margin of error.
Enter one through two thousand finite numeric observations using commas, whitespace or new lines, optionally scientific E notation. Values are bounded in magnitude, sample N<2 is rejected and selected precision affects display only.