How Can Documentation Explain an Uncertainty Range?
From the earlier reference collection. Read the current software blog.
Define how endpoints are calculated and what the interval means before readers use it as a measure of confidence.
Define the quantity and interval
An uncertainty range is useful only when readers know what quantity it surrounds and how its endpoints were produced. Identify the central value, lower bound, upper bound, and units. Say whether the interval is a measurement tolerance, model range, forecast spread, observed minimum and maximum, or another construct. Those descriptions are not interchangeable.
For example, a displayed estimate of 12 with a range from 10 to 14 could mean that repeated measurements varied across those values, or that a model produced a particular interval. The numbers alone do not tell the reader which interpretation applies. Name the method and the data that went into it.
Explain the derivation
Describe the calculation in enough detail for a user to reproduce or assess it. If the range comes from instrument specifications, identify the relevant tolerance and whether it applies to the whole system. If it comes from observed values, state the sample period and rule used to select the endpoints. If it comes from a statistical method, name the interval method and confidence or coverage level only when those are actually defined.
A practical note might say: “The band shows the minimum and maximum of five readings collected during the stated interval.” That is interpretable and does not imply a probability model. By contrast, calling it a 95 percent interval would require a defined method and assumptions that support that statement.
Describe limitations and exclusions
State what the range does not capture. A sensor tolerance may not include errors from placement or calibration. A forecast spread may omit unusual events not represented in the model. A range based on observed values does not guarantee that future readings will remain inside it. Describe missing data, rounding, and any filters that can narrow or shift the interval.
For a chart, explain whether endpoints are calculated before or after aggregation. If daily averages are shown with a range of hourly values, make that relationship explicit. Otherwise readers may assume the band represents uncertainty around the average when it actually shows variation over time.
Show a worked interpretation
Walk through one example in plain language. If a measured value is 12 units with a stated instrument tolerance of plus or minus 1, the documented range is 11 to 13 units under that tolerance model. Explain that this range does not account for other sources of error unless they are included. Avoid presenting the interval as a guarantee about the true value.
End with guidance for use: what decisions the range can inform, and what additional evidence a high-stakes decision would require. Link to the calculation details or methodology version so readers can check the assumptions. A clear explanation turns a band on a graph into a defined statement with visible limits.