Executive answer
The interquartile range contains the central part of an ordered sample and reduces the weight of extreme observations. The median is the midpoint. In transfer pricing, both become meaningful only after demonstrating that transactions or companies are comparable, the indicator is calculated consistently and the tested-party result relates to the same transaction and period.
Article 180 of the Mexican Income Tax Law provides that when two or more comparable transactions exist, a range adjusted through statistical methods may be obtained. A price, consideration or margin inside the range is regarded as independent; when outside, the statutory rule refers to the median. Apply that text together with current rules and the facts. It does not turn any company list into a valid range or explain how an adjustment should be executed.
Before moving profit, review three layers: benchmark quality, accuracy of the tested result and adjustment nature. A deviation may arise from accounting, segmentation, exchange rate, an extraordinary event, actual function or a deficient policy. Adjusting without diagnosis may fix the number and preserve the problem.
Basic concepts
Order comparable results from low to high. The median divides the sample in half. The first quartile marks the lower central boundary; the third marks the upper central boundary. The interval between them is the interquartile range. Exact position formulas differ by statistical convention; state the method and apply it consistently.
Do not confuse the full minimum-to-maximum range with the interquartile range. Do not confuse mean and median. The mean is the sum divided by observations and is sensitive to extremes; the median depends on rank.
A small or heterogeneous sample can produce mathematical quartiles without economic comparability. Statistics do not replace qualitative review.
Preconditions
Delineated transaction
Define dealing, parties, period, functions, assets, risks, agreement and conduct. The indicator should test that transaction, not an uncontrolled mixture.
Selected method
The range results from an appropriate method. Do not select a method because it produces a convenient interval. Document CUP rejection and tested-party choice where relevant.
Reliable sample
Review internal comparables, search, screens, related parties, losses, functions, intangibles, markets and segmentation. Preserve rejection and comparability-adjustment decisions.
Consistent indicator
Define numerator and denominator. Revenue, operating costs, depreciation, extraordinary items and assets should be treated comparably. Reconcile the tested-party indicator to financial statements.
Comparable period
Determine whether one year, a multiple-year average or another window is used and why. Do not compare an annual result with an average range without explanation.
Illustrative example
Assume a reviewed sample with seven operating margins: 2.0%, 3.1%, 4.0%, 4.8%, 5.5%, 6.7% and 8.2%. The observed median is 4.8%. Quartiles depend on the statistical convention; the file should show the formula, data and result.
If the tested party earns 3.6%, do not compare only with the median. First determine whether it falls inside the properly calculated range. If it earns 1.2%, it is below every observation and needs immediate diagnosis. The economic difference can be estimated by applying the relevant target to the tested denominator, while tax and accounting effects require separate analysis.
For return on sales, if segmented revenue is 100 and current profit is 1.2, the margin is 1.2%. An illustrative median of 4.8% implies profit of 4.8 and a difference of 3.6 before taxes, currency, withholding, VAT or other effects. That is not an automatic invoicing instruction.
Static exposure calculator
| Input | Question | Validation |
|---|---|---|
| Indicator | ROS, markup, return on assets or another? | Aligned with function |
| Denominator | Segmented sales, costs or assets? | Reconciled to statements |
| Current result | Same definitions and period? | Recalculated |
| Q1, median and Q3 | From the approved sample? | Formula and version |
| Position | Inside, below or above? | No premature rounding |
| Target difference | What amount reaches the applicable point? | Reproducible calculation |
| Effects | Income tax, invoice, VAT, withholding, customs? | Layer-by-layer review |
| Execution | Real, virtual, corresponding or late? | Rule and approval |
A future interactive version can model scenarios, but should prevent calculation until the method, segment and period are confirmed.
If closing reveals a deviation, validate the benchmark, indicator and segment before turning a statistical difference into an invoice or entry.
Inside the range does not mean risk-free
A result inside the range addresses price or margin under the analysis used. It does not prove that a service existed, an expense is deductible, an agreement matches conduct, withholding was correct or the return is complete.
The range itself may be weak because companies are not comparable, indicators differ or the segment was manipulated. Mathematical position does not cure those failures. Preserve materiality, agreements and performance evidence.
If the result changes materially between years while remaining inside, investigate the operating cause. Monitoring aims to understand and prevent deviation, not only stay within the interval.
Outside the range: decision sequence
- Recalculate. Verify formulas, signs, currency, period and rounding.
- Reconcile. Connect the segment to the ledger and remove duplicates or misclassification.
- Review comparables. Confirm sample, independence, updates and adjustments.
- Explain facts. Identify the risk, event or functional change causing deviation.
- Determine the rule. Analyze Article 180 and current annual rules.
- Model the amount. Calculate the target and tax effects.
- Classify the adjustment. Real, virtual, voluntary, primary, corresponding or late as applicable.
- Coordinate the counterparty. Confirm document, entry and effect.
- Approve. CFO, tax, accounting and other functions.
- Document the cause. Fix policy or process for the next period.
Do not jump from step one to six. The deviation may show that the denominator is wrong or that the entity controlled an unexpected risk.
Median and target point
Where the applicable provision requires the median for an out-of-range result, distinguish the legal rule from management policy. During the year, a company may manage to an internal target or band to reduce volatility; that policy does not itself change the tax rule.
Do not use a range edge automatically because it needs a smaller adjustment. Document the legal and economic basis for the point. Likewise, do not move an inside-range result to the median without assessing whether the additional payment is arm’s length and deductible.
Rounding matters. Calculate at full precision and show the display convention. Small rounding differences can change classification near Q1 or Q3.
Multiple-year averages
Multiple-year information may illuminate cycles, but the obligation and tested result relate to specific fiscal years. Distinguish the comparable average, tested-party average and current-year test. Explain why the business cycle requires several periods.
Do not automatically offset an out-of-range year with an inside-range year. Analyze law, method and facts. An exceptional loss may be valid when local management controlled the risk; averaging does not replace that proof.
Retain annual data and a change bridge. If comparable data are updated later, record what was available when the report was prepared and how the new data affect the conclusion.
Ranges under different methods
Under CUP, a range may contain prices, rates or consideration and demands comparable terms. Under resale price or cost plus, gross margins are highly sensitive to accounting. Under TNMM, ranges often apply to net indicators over sales, costs or assets. Under profit split, a range may require a different design based on contributions.
Do not transfer quartiles from one indicator to another. A 4% return on sales is not a 4% markup on costs. Convert only with consistent data and formulas.
Common errors
- Calculating quartiles before approving the sample.
- Using spreadsheet formulas without documenting convention or version.
- Comparing an annual indicator with an incompatible multiple-year range.
- Rounding before classifying position.
- Adjusting to an edge without authority.
- Moving an inside-range result merely to shift profit.
- Ignoring indirect tax and customs.
- Treating an out-of-range result as an automatic penalty.
- Failing to coordinate the counterparty effect.
- Repeating the same true-up without fixing policy.
Preventive monitoring
Calculate an operating range from the budget and refresh it monthly or quarterly. Separate volume, price, mix, cost, currency and extraordinary variance. Forecast closing and define escalation thresholds.
The dashboard should show actual result, forecast, Q1, median, Q3, distance, cause and owner. Final comparables are not needed to flag an obvious deviation, but a tax adjustment should use a validated analysis.
Quality control
A second reviewer reproduces ordering, quartiles, median, indicator and difference. They verify duplicates, segment reconciliation and that the range belongs to the approved sample. Tax reviews the rule; accounting execution; legal the agreement; customs and VAT their respective effects.
The final memorandum separates fact, calculation, law, decision and action. Preserve the data file, formulas and approval.
Bridge from statistics to the journal entry
Before booking, prepare a bridge showing original accounting result, accepted reclassifications, segmented result, indicator, applicable point, target amount and difference. Then add invoice or document, counterparty, currency, exchange rate, period, tax and account. This allows a reviewer to distinguish a data correction from a tax decision.
If the counterparty calculates over a different base, resolve the difference before invoicing. Confirm that both parties will use the same gross amount, period and characterization. Record any asymmetry and its remediation route.
After adjustment, recalculate the indicator and retain evidence that it reaches the approved result. Reconcile the entry to the report and returns. An authorized true-up that is posted incorrectly leaves the exposure unresolved.
Related topics
- PT-018 and PT-019: comparability and method.
- PT-025: TNMM and indicator.
- PT-026 and PT-027: year-end adjustments and classification.
Pre-close simulation
Build a workpaper showing each comparable’s indicator, ordering, quartiles, median, tested result and distance from the range. Lock formulas and sources. Then simulate revenue, cost, exchange rate, reclassifications and removed comparables to identify what drives the deviation. The calculator illustrates a decision; it does not replace functional analysis or the applicable rule.
Reconcile numerator and denominator to segmented accounting. Review signs, averages and exceptional items. If the result falls outside the range, document whether facts support a loss, whether an accounting or tax adjustment exists, and the relevant amount. Do not automatically turn the median into an operating target without considering period and policy.
The CFO receives scenarios, amount, deadline, connected effects and recommendation. Preserve versions before and after any adjustment. A simple-looking statistic can then be traced to data, judgment and an approved decision.
Sources and verification date
- Mexican Income Tax Law, current text, Articles 179 and 180.
- 2026 Miscellaneous Tax Resolution, applicable adjustment rules and subsequent amendments.
- OECD Mexico Transfer Pricing Country Profile.
Sources checked on August 2, 2026. The statistical formula and adjustment treatment should be validated for the specific fiscal year and facts.
Request a Range Review to recalculate the sample, quartiles, indicator, exposure and coordinated adjustment route.