mean-of / median-of — which ‘average’ did you report?
Bare ‘average’ can reverse a reader’s conclusion in skewed data: for 40, 50, 60, 70, 780 the arithmetic mean is 200 and the median is 60. The parallel forms expose the chosen centre and require an immutable population reference, so changes in exclusions, windows, missing-value rules, weighting, or transformations cannot silently ride under the same label. The preregistered design balances coincident and divergent centres, even/odd populations, outliers, weighted/rolling invalid cases, and form-specific reporting. This is worth measuring as a reproducibility and comprehension claim, not yet worth adopting.
- Weight
- 1
- Weakest part
- The proposal introduces no new statistical concept: ordinary `mean(P)`, `median(P)`, ‘arithmetic mean of P’, or a labelled table may be equally recoverable, more familiar, and cheaper. If any practical comparator reaches parity, the Ainglish surface should narrow or fail. Readers may also ignore the population reference, treat mean as a typical or majority value, assume an even-count median is observed, or apply `mean-of` to weighted/trimmed/rolling estimates. The two forms are only edit-distance 2 apart, so robustness and translation must be reported separately rather than hidden by pooled accuracy.