Bound a Mean without Inventing Missing Values

How to Use This Tool

Compute best and worst feasible means from declared value bounds rather than one imputed guess. Estimate the feasible mean range when observations are missing, using the observed sum, count and explicit minimum and maximum bounds.

The decision this tool supports

Replacing every missing value with one average hides how much the conclusion depends on an untested assumption about unobserved records. This page keeps the decision bounded to feasible mean range width and the supporting outputs shown beside it. Missing Data Range does not import an account, infer a market rate, or silently substitute an industry average.

Inputs and units

The Missing Data Range calculation uses Observed value sum, Observed count, Missing count, Minimum feasible value, Maximum feasible value. Keep all money values in one currency and all time, distance, mass, energy or volume entries in the unit printed beside the field. Mixing Missing Data Range scopes can produce a plausible number with the wrong meaning.

• Observed value sum is entered in sum.
• Observed count is entered in records.
• Missing count is entered in records.
• Minimum feasible value is entered in value.
• Maximum feasible value is entered in value.

Formula and worked check

Worst mean = (observed sum + missing count × minimum) ÷ total count; best mean substitutes maximum; range width is best minus worst. An observed sum of 720 across 80 records with 20 missing bounded from 0 to 10 yields feasible means from 7.2 to 9.2, width 2.0. The Missing Data Range default is an executable known-answer case, not a benchmark or recommendation. Change one input and verify that the direction of feasible mean range width still matches the stated relationship.

How to interpret the result

If the decision changes anywhere inside the range, investigate missingness or use a justified statistical model instead of reporting the midpoint as fact. The additional Missing Data Range outputs expose the denominator, comparison, capacity or reverse value needed to audit the primary result instead of presenting one unexplained number.

Assumptions

• Every missing value lies within the entered bounds.
• Observed sum and counts describe the same metric.
• The mean is the decision statistic under review.

Save the Missing Data Range input values and date with any material decision. A later Missing Data Range rerun is reproducible only when the same assumptions and units are available.

Limitations and safety boundary

Bounds do not describe probability, missingness mechanism, sampling bias, multivariate relationships, uncertainty intervals or a recommended imputation. Missing Data Range is an estimate and cannot replace a contract, local code, licensed professional, calibrated measurement, lender statement or platform report where one governs the decision.

Source and privacy

The Missing Data Range definition or rule was checked against NIST Guide for Conducting Risk Assessments on 2026-08-26. Recheck NIST Guide for Conducting Risk Assessments when a specification or policy behind Missing Data Range can change. Missing Data Range arithmetic runs in this browser tab; ecech does not receive the values through a calculation API.