What is the interquartile range?

The interquartile range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset, capturing the middle 50% of observations. It is a robust measure of statistical spread because it ignores the top and bottom quartiles, making it insensitive to outliers and extreme tail values.

How does the interquartile range differ from standard deviation?

The interquartile range measures spread using percentiles and is robust to outliers, while standard deviation measures spread around the mean and is highly sensitive to extreme values. A single crisis observation can inflate standard deviation dramatically but leaves the IQR largely unchanged, which is why desks prefer IQR for skewed financial series.

What does 'outside the historical interquartile range' mean?

'Outside the historical interquartile range' means a current reading sits above the 75th percentile or below the 25th percentile of its own past observations. For valuation screens, it flags that today's metric is richer or cheaper than three-quarters of historical values — a concise way to signal stretched positioning without asserting a precise tail probability.

Why does the interquartile range matter for valuation analysis?

The interquartile range matters because it benchmarks a current valuation against its full historical distribution robustly, resisting distortion from crash or bubble outliers. In 2025-2026, analysts cite forward P/E and equity risk premia sitting 'outside the historical IQR' to flag that index valuations — concentrated in the Magnificent Seven — are richer than most of their own history.

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Glossary

interquartile range

IQR · middle 50% · 25th-to-75th percentile range · 10th-90th percentile band · P10-P90 range · 10-90 range

Macro Frameworks

The interquartile range (IQR) is the span between the 25th and 75th percentiles of a distribution — the middle 50% of observations. It measures statistical dispersion robust to outliers, summarizing where the bulk of a series sits without being distorted by tail values.

How it works

Rank-order the data, find Q1 (25th percentile) and Q3 (75th percentile); IQR = Q3 − Q1. Because it discards the top and bottom quartiles, it is unaffected by extreme observations, unlike standard deviation. On a macro desk it benchmarks where a current reading sits versus its own history — "outside the historical IQR" means the present value exceeds the 75th (or undershoots the 25th) percentile of past observations.

Why it matters now

In 2025-2026, equity valuation screens — forward P/E, earnings yield, equity risk premium — sit "outside the historical IQR" for the Magnificent Seven and the index they dominate, the canonical desk shorthand for stretched but not yet mean-reverting positioning.

Example

If the S&P 500's forward P/E has historically ranged with Q1 = 14x and Q3 = 18x (IQR = 4x), a current 22x multiple sits well outside the historical IQR — above the 75th percentile by a full range-width. The phrasing flags that today's reading is richer than three-quarters of all historical observations, without claiming a precise tail probability.

Mechanism

IQR = Q3 − Q1, where Q1 = 25th percentile, Q3 = 75th percentile

How desks use it

Benchmarking a current valuation multiple against its own historical percentile distribution
Flagging stretched positioning robustly, ignoring crisis-era outliers that distort standard deviation
Reading SEP or analyst forecast dispersion as a fan of quartiles

Frequently asked

What is the interquartile range?: The interquartile range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset, capturing the middle 50% of observations. It is a robust measure of statistical spread because it ignores the top and bottom quartiles, making it insensitive to outliers and extreme tail values.
How does the interquartile range differ from standard deviation?: The interquartile range measures spread using percentiles and is robust to outliers, while standard deviation measures spread around the mean and is highly sensitive to extreme values. A single crisis observation can inflate standard deviation dramatically but leaves the IQR largely unchanged, which is why desks prefer IQR for skewed financial series.
What does 'outside the historical interquartile range' mean?: 'Outside the historical interquartile range' means a current reading sits above the 75th percentile or below the 25th percentile of its own past observations. For valuation screens, it flags that today's metric is richer or cheaper than three-quarters of historical values — a concise way to signal stretched positioning without asserting a precise tail probability.
Why does the interquartile range matter for valuation analysis?: The interquartile range matters because it benchmarks a current valuation against its full historical distribution robustly, resisting distortion from crash or bubble outliers. In 2025-2026, analysts cite forward P/E and equity risk premia sitting 'outside the historical IQR' to flag that index valuations — concentrated in the Magnificent Seven — are richer than most of their own history.

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