Measure hidden direction across ordered observations precisely. Center averages correctly for even and odd windows. Reveal smoother trend signals with cleaner comparisons for decisions.
Results appear above the form for quick review.
| Time | Actual Value | Centered Moving Average | Residual | % Difference |
|---|---|---|---|---|
| 1 | 120.0000 | — | — | — |
| 2 | 128.0000 | — | — | — |
| 3 | 133.0000 | 135.2500 | -2.2500 | -1.6917% |
| 4 | 145.0000 | 142.7500 | 2.2500 | 1.5517% |
| 5 | 150.0000 | 150.1250 | -0.1250 | -0.0833% |
| 6 | 158.0000 | 156.8750 | 1.1250 | 0.7120% |
| 7 | 162.0000 | 163.2500 | -1.2500 | -0.7716% |
| 8 | 170.0000 | 169.7500 | 0.2500 | 0.1471% |
| 9 | 176.0000 | 176.5000 | -0.5000 | -0.2841% |
| 10 | 184.0000 | 183.5000 | 0.5000 | 0.2717% |
| 11 | 190.0000 | — | — | — |
| 12 | 198.0000 | — | — | — |
| Time | Observed Value | Comment |
|---|---|---|
| 1 | 120 | Starting level |
| 2 | 128 | Moderate increase |
| 3 | 133 | Growth continues |
| 4 | 145 | Short acceleration |
| 5 | 150 | Trend still rising |
| 6 | 158 | Stable improvement |
Step 1: Simple moving average
For a window length m, each moving average is:
MA = (x₁ + x₂ + ... + xₘ) / m
Step 2: Centering rule for odd periods
If m is odd, the moving average already aligns with the middle observation.
Step 3: Centering rule for even periods
If m is even, first compute the moving averages, then average each adjacent pair:
CMA = (MAᵢ + MAᵢ₊₁) / 2
This creates a centered value aligned to a real time position, which is ideal for trend extraction in seasonal or indexed data.
It smooths short-term noise and highlights the middle trend of a time series. This makes long-term direction easier to inspect, especially in seasonal or irregular data.
Even-length windows fall between two observations. Centering averages adjacent moving averages, so the smoothed value aligns with a true time point in the series.
Yes. Odd windows center naturally on a middle observation. Even windows need a second averaging step, and this calculator performs that automatically.
Ordered numeric data works best, such as monthly sales, traffic, production, or indexed business metrics. Keep the values in their original chronological order.
Centered averages require enough surrounding points. Near the beginning and end of the series, the full window is unavailable, so those positions stay empty.
The residual equals actual value minus centered moving average. It helps you inspect how far each observation sits above or below the smoothed trend.
Pick a period that matches your analysis goal. Short windows react faster, while longer windows smooth more aggressively and highlight broader movement.
Yes. The calculator includes CSV export for spreadsheets and PDF export for printable summaries, making it easier to document or share findings.
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.