Interquartile Range (IQR): The OECD Arm's Length Range
The interquartile range defined: the band between the first and third quartiles of the comparable pool — the OECD\'s preferred construction of the arm's length range.
Definition
The interquartile range (IQR) is the band between the first quartile (25th percentile) and the third quartile (75th percentile) of a set of values. In transfer pricing it is the OECD’s preferred construction of the arm’s length range (Ch. 3, para 6.104): the band of the comparable pool’s PLI values that the statistical evidence treats as the arm’s length zone, robust to the outliers that no qualitative screen fully eliminates.
Formula
Sort the pool's PLI values ascending
Q1 = median of the lower half (excluding the overall median)
Q3 = median of the upper half (excluding the overall median)
IQR = [Q1, Q3]Worked example, nine OP/OC values (3.2, 3.6, 4.0, 4.5, 4.8, 5.1, 5.4, 5.9, 6.3%): median 4.8; Q1 = median(3.2, 3.6, 4.0, 4.5) = 3.8; Q3 = median(5.1, 5.4, 5.9, 6.3) = 5.65. IQR: 3.80%–5.65%.
Why the IQR rather than the full range
The IQR discards the outer 25% of the pool on each side — the companies that are in the pool but least comparable. That tolerance is the point: a qualitative screen is a judgment, and the IQR is the statistical admission that some judgment error survives. The full range (pool min to max) is maximally sensitive to exactly those companies; the IQR is the defensible middle, which is why it is the default position.
The construction choice (which quartile convention, how even samples are halved) must be consistent across studies and stated in the file — the convention is a method, and a method is documented.
See also
FAQ
Is the IQR a legal requirement in India? No — it is the OECD’s statistical recommendation, and the position Indian practice increasingly treats as the default. The full range remains in use (small pools, secondary arguments); defensibility comes from the documented choice, not the label.
What happens to a tested party outside the IQR but inside the full range? The IQR is the position; the placement outside it is analysed — unadjusted comparability differences, pool adequacy, tested party appropriateness — rather than answered by silently switching to the full range. The switch after seeing the number is the error; the analysis before it is the discipline.
Run the screens as a study, not a spreadsheet
Quartyl applies the method, PLI and screening steps above as a pipeline — and keeps a documented reason for every exclusion.
Related docs
Arm's Length Range: IQR, Mid-Point and Testing the Price
The arm's length range defined: the band of acceptable profit levels derived from comparables, usually the interquartile range, and how a tested party is placed inside it.
Read docIQR vs Full Range: Choosing the Arm's Length Range
OECD's interquartile range versus the full range: quartile math step-by-step, when each is defensible, the mid-point argument, and how to document the choice in India.
Read doc