Direct Answer
The interquartile range, or IQR, is the distance between the third and first quartiles, so it covers the middle half of the observations in the window. It is a dispersion measure that ignores the extreme tails. A larger value means the central half of the data is more spread out.
Interquartile Range: Formula, Meaning, Signals, Examples and How to Use It
How Is Interquartile Range Calculated?
The interquartile range, or IQR, is the distance between the third and first quartiles, so it covers the middle half of the observations in the window. It is a dispersion measure that ignores the extreme tails.
Formula: IQR = Q3 - Q1; Tukey outlier fences are Q1 - 1.5*IQR and Q3 + 1.5*IQR
Inputs:
- Series values
- Window length
- First and third quartiles
Worked example. A third quartile of 118 and a first quartile of 102 give an interquartile range of 16. The inputs are illustrative numbers, not market data.
Reading it. A larger value means the central half of the data is more spread out. Because it excludes the top and bottom quarters it barely responds to a few extreme values, and values beyond the Tukey fences are conventionally flagged as outliers.
Limits. It discards information about tail behavior, which is exactly what matters for risk. Quartile calculation conventions differ slightly between software.
What is Interquartile Range?
The interquartile range, or IQR, is the distance between the third and first quartiles, so it covers the middle half of the observations in the window. It is a dispersion measure that ignores the extreme tails.
How to use Interquartile Range
A larger value means the central half of the data is more spread out. Because it excludes the top and bottom quarters it barely responds to a few extreme values, and values beyond the Tukey fences are conventionally flagged as outliers. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Q3 minus Q1 covers the middle half of observations, so a few extreme values cannot widen it.
- The 1.5 times IQR fences give a rule for flagging outliers that uses the data's own spread.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- It uses only two quantiles, so it is a coarse estimate of spread compared with measures that use every value.
- In windows with fewer than a few dozen values the quartile positions are interpolated between very few points.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Interquartile Range a buy or sell signal?
No. A larger value means the central half of the data is more spread out. It discards information about tail behavior, which is exactly what matters for risk. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Interquartile Range?
Interquartile Range takes these inputs: series values; window length; first and third quartiles. There is no universal best setting for the tunable ones, so test them across instruments, regimes and out-of-sample periods and favor stable parameter regions over one historical winner.
Can Interquartile Range be used by itself?
It discards information about tail behavior, which is exactly what matters for risk. Quartile calculation conventions differ slightly between software. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Interquartile Range work on every timeframe?
The calculation (IQR = Q3 - Q1; Tukey outlier fences are Q1 - 1.5*IQR and Q3 + 1.5*IQR) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Interquartile Range give false signals?
It uses only two quantiles, so it is a coarse estimate of spread compared with measures that use every value. In windows with fewer than a few dozen values the quartile positions are interpolated between very few points. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Interquartile Range be backtested?
Rebuild Interquartile Range from series values using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.