Analyze stochastic signals using flexible variance estimators today. Enter time series, add weights, view plots. Get clear results above the form in seconds now.
Paste values as comma or newline separated numbers. Use weights for frequency or importance weighting.
Use these values to test the calculator quickly.
| Index | Sample value | Weight |
|---|---|---|
| 1 | 2.10 | 1 |
| 2 | 2.40 | 1 |
| 3 | 2.20 | 2 |
| 4 | 2.60 | 1 |
| 5 | 2.50 | 1 |
| 6 | 2.30 | 1 |
| 7 | 2.80 | 1 |
| 8 | 2.70 | 2 |
For time‑ordered samples, autocovariance lag 1 is also reported for unweighted inputs.
Variance summarizes spread in a random process. It is reported in squared units. Large variance often signals unstable dynamics. Small variance suggests tight control. Use it for sensor noise, finance returns, and network latency.
Use the unbiased sample estimator for measured samples. It divides by N minus one. Use the population estimator for complete populations. It divides by N. When N is small, estimator choice matters more. Report the estimator with the value.
Weights act like repeated observations. A weight of two doubles influence. Total weight equals the sum of weights. The calculator validates nonnegative weights. Frequency-unbiased correction reduces small weight bias. It multiplies by Σw divided by Σw minus one.
Standard deviation is the square root of variance. It returns to original units. Range shows max minus min. Coefficient of variation scales dispersion by mean. A CV near zero means stable magnitude. A high CV suggests large relative swings. Keep units consistent across datasets. That improves comparisons and dashboards.
The line chart shows values over index order. The mean line provides a baseline. Dotted bands show plus or minus one standard deviation. Outliers often cross the bands. Sustained drift may indicate nonstationary behavior. Sudden spikes can inflate variance quickly. Lag one autocovariance helps assess short memory patterns. Weighted markers appear larger when weights increase. This highlights dominant segments.
Download CSV for spreadsheets and pipelines. Download PDF for quick sharing. The table lists deviations and squared deviations. These values verify manual checks. Store exported files with timestamps. This supports repeatable quality reviews. Use the same precision during reruns. It prevents rounding disputes in reports.
It measures average squared deviation from the process mean. It quantifies spread in time series samples. Higher variance indicates more volatility.
Use unbiased sample variance for sampled observations. Use population variance for complete populations. Use weighted options when values have frequencies or importance.
Variance is usually defined around the mean. Removing it isolates fluctuations. If you disable it, variance is computed around zero instead.
Yes. Weighted mean shifts toward higher-weight samples. Weighted variance emphasizes those samples too. This is useful for frequency tables and reliability scoring.
It is standard deviation divided by the absolute mean. It is shown as a percentage. It helps compare dispersion across signals with different scales.
The PDF is generated without external libraries. It focuses on essential metrics and the verification table. Use CSV when you need richer formatting.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.