GlossaryStatistics and interpretation
Rolling average
A rolling average summarizes successive windows of observations. Learn how window length, placement, missing data, and revisions affect the line.
A rolling average is an average recalculated over a moving window of observations. Each new calculation advances the window, adding newer values and dropping older ones. It smooths short-term fluctuations so broader patterns can be easier to see, while changing how individual peaks and recent changes appear.
Specify the window
A seven-day trailing average usually uses the current day and the six preceding days. A centered average places the window around a date instead. Those methods position the same information differently and are not interchangeable at the end of a series.
NIST's statistical handbook explains the moving-average calculation as averaging successive smaller sets and advancing one period at a time. Its separate centered-average discussion shows why the placement of the result matters. NIST moving-average explanation.
Example
Hypothetical example: A department records daily eligible call totals of 10, 20, and 30. The trailing three-day average on day three is 20 calls per day. Day four brings 40 calls, so the next average uses 20, 30, and 40 and becomes 30.
The day-four average is not that day's call count, which is 40. It summarizes three days. Adjacent averages share two of their three observations, so they are not independent descriptions of entirely separate activity.
Common confusion
A rolling average differs from a rolling total. The three-day total in the second window is 90 calls; its daily average is 30. Labeling one as the other changes the scale by a factor of three.
Smoothing also does not remove errors or reporting delays. If yesterday's data are incomplete, the newest average can be incomplete too. A later backfill can revise several displayed averages because each affected observation belongs to multiple windows.
What a smooth line can hide
Longer windows produce more smoothing and can make a sudden change appear more gradual. A trailing average also incorporates older activity, so its movement may follow a change in the daily counts. Keep the original daily or monthly figures available when individual peaks matter.
Explain how missing observations are handled. Treating a missing day as zero lowers the average without evidence of zero activity; averaging only available days changes the effective window. For unequal period lengths or other weights, describe the method rather than calling it a simple rolling average. The window, weighting, and date placement should be clear in the chart's notes.