Calculation Results
Your rolling statistics appear below.
Moving Std Deviation Trend
| # | Window | Anchor Index | Mean | Variance | Std Deviation | Scaled Std Deviation | CV % | Window Values |
|---|
Calculator
Formula Used
Step 1: Window Mean
For each rolling window of size n, compute the mean: μ = (Σxᵢ) / n.
Step 2: Variance
Population variance: σ² = Σ(xᵢ - μ)² / n
Sample variance: s² = Σ(xᵢ - μ)² / (n - 1)
Step 3: Standard Deviation
Population standard deviation: σ = √σ²
Sample standard deviation: s = √s²
Step 4: Scaled Output
If a scale factor is applied, the calculator returns: Scaled Std Deviation = Std Deviation × Scale Factor.
How to Use This Calculator
- Paste your ordered numeric series into the data field.
- Choose a window size based on how much smoothing you need.
- Select sample or population mode for your variance calculation.
- Pick trailing, centered, or leading alignment for the window anchor.
- Set the decimal precision and scale factor if needed.
- Choose auto detect or a manual delimiter mode.
- Press the calculate button to see the result section above the form.
- Download the full results as CSV or PDF when needed.
Example Data Table
Example series with a window size of 3. This helps illustrate how rolling spread changes across consecutive observations.
| Index | Value | Window Example |
|---|---|---|
| 1 | 10 | 10, 12, 13 |
| 2 | 12 | 12, 13, 11 |
| 3 | 13 | 13, 11, 14 |
| 4 | 11 | 11, 14, 15 |
| 5 | 14 | 14, 15, 18 |
| 6 | 15 | 15, 18, 17 |
| 7 | 18 | 18, 17, 16 |
| 8 | 17 | 17, 16, 20 |
| 9 | 16 | — |
| 10 | 20 | — |
FAQs
1) What does moving standard deviation measure?
It measures how much values vary inside each rolling window. Higher values show greater short-term spread, while lower values show tighter clustering around the local mean.
2) When should I use sample mode?
Use sample mode when your window is treated as a sample from a larger process. It divides by n-1, which is common in statistical estimation.
3) When should I use population mode?
Use population mode when each rolling window contains the full set of observations you want to evaluate. It divides by n and reports the direct spread of that window.
4) What does window alignment change?
Alignment changes the index assigned to each result. Trailing anchors at the end, leading anchors at the start, and centered anchors near the middle.
5) Why is my window size important?
Smaller windows react faster to local changes. Larger windows smooth the series more and reduce short-term noise, but they can hide sudden shifts.
6) What is the scale factor for?
The scale factor multiplies each rolling standard deviation. It is useful when you want adjusted bands, custom thresholds, or quick scenario comparisons.
7) Can I use decimals and negative values?
Yes. The calculator accepts decimals, negative values, and scientific notation, as long as each entry is a valid number in the selected delimiter format.
8) What does CV % mean in the results?
CV means coefficient of variation. It compares standard deviation to the absolute mean, expressed as a percentage, which helps compare relative variability across windows.