Keep the starting amount beside every percentage
A percentage change has a base. A move from 100 to 200 USD is 100%, while a move from 1000 to 900 USD is−10%. The relative changes and the dollar changes describe different features of the same two fictional series.
Before averaging, state what each observation represents and which weights are intended. Equal weight per series is a valid declared statistic, but it should not be presented as an amount-weighted aggregate when the starting amounts differ.
Calculate two explicitly different teaching summaries
The equal-weight arithmetic mean of+100% and−10% is+45%. Pooling the compatible starting dollar amounts instead gives 1100 USD, with pooled ending amounts also 1100 USD. Under the closed model, pooled change is 0%.
There is no contradiction: the calculations use different weighting. The small starting series receives the same weight as the large one in the first summary. In the pooled comparison, each starting dollar contributes to the aggregate base.
| Teaching summary | Inputs and weights | Result |
|---|---|---|
| Equal-weight percentage mean | (100% − 10%) / 2 | 45% |
| Pooled dollar comparison | 1100 USD → 1100 USD | 0% |
| Actual portfolio return | Cash flows and scope not supplied | Not established |
Pool amounts only when their units and scope are compatible
The example assumes the two figures have the same USD unit, compatible endpoint times and no transfers or other movements. Mixing token quantities with dollar values or unrelated date windows would invalidate the simple pooled sum. Preserve conversion and timing evidence before combining real records.
Also distinguish two separate series from two consecutive returns on one balance. Consecutive relative changes compound on a changing base; they are not pooled in the same way as two simultaneous entered holdings. A label saying average should not conceal which operation was performed.
Do not use an average to conceal a missing denominator
If one starting amount is zero, its ordinary percentage-change calculation has a zero denominator. If an endpoint is missing, neither its relative nor dollar change is established. Preserve those states rather than filling them with zero to maintain a neat two-row average.
The NIST definition of an arithmetic mean specifies a sum divided by observation count. It does not choose the observation unit, establish an investment return methodology or justify replacing a missing value. Those decisions belong in the declared comparison.
Name the statistic you actually calculated
A reproducible report can state 45% as an equal-weight mean of two entered relative changes and 0% as a separate pooled comparison under the listed assumptions. Keep the two numbers with their labels instead of selecting whichever sounds more attractive.
All values here are fictional. The article does not authenticate holdings, calculate a cash-flow-adjusted portfolio result, rank investments or predict an outcome. It adds a weighting audit to a percentage-comparison workflow without requiring a trading account.
The optional link below leads to this site's separate crypto signals and Telegram updates offer. The record method is usable without that offer. It does not independently verify the offer, establish country eligibility or turn the teaching example into an actual transaction.
Primary sources and scope
- NIST/SEMATECH: Measures of Location
Arithmetic mean uses the sum divided by the count of observations. The worked cases here are invented, not evidence of performance. Checked 2026-10-21.