Primary result
Interquartile range
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IQR
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Enter numbers to calculate quartiles.
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Statistics
IQR Calculator
Find quartiles, interquartile range, and outlier fences from any dataset.
Comma, space, and line separated numbers are accepted. Non-numeric text is ignored.
Q1
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Median
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Q3
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Outliers
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IQR Calculator: Read Spread, Spot Outliers, and Understand Quartiles
The interquartile range is one of the most useful measures of spread in statistics because it focuses on the middle 50% of the data instead of getting dragged around by extremes. Students use it in box-and-whisker plots, analysts use it to compare variability, and anyone cleaning a dataset uses it to separate normal spread from outliers. If the goal is to understand the typical width of the data rather than its full range, IQR is the right metric.
The niche vocabulary is quartiles, median, fences, and outliers. The calculator uses the standard Tukey-style idea of taking Q1 from the lower half, Q3 from the upper half, and then subtracting the two to get the IQR.
The Math: The Core Rule Explained
The Core Equation
IQR = Q3 - Q1
| Metric | Definition | Use |
|---|---|---|
| Q1 | 25th percentile | Lower quartile |
| Q3 | 75th percentile | Upper quartile |
| Fences | Q1 - 1.5×IQR, Q3 + 1.5×IQR | Outlier screening |
Real-World Use Case
A classroom dataset can look tightly packed on a histogram but still have a few extreme points. The IQR gives a cleaner picture of the center mass. A business dataset can use the same logic to compare sales consistency across locations without letting one unusual day dominate the summary.
The lower and upper fences are also useful because they provide an explicit outlier rule instead of a vague impression. That is the practical reason the calculator shows fences as well as the IQR itself.
When you need to explain spread in plain English, IQR is the number that says how wide the middle of the dataset really is.
Frequently Asked Questions
How is IQR different from range?
Range uses only the minimum and maximum. IQR focuses on the middle half of the data and is much less sensitive to extreme values.
What is a fence?
A fence is the cutoff used to label likely outliers: Q1 - 1.5×IQR and Q3 + 1.5×IQR.
Do odd and even lists work?
Yes. The calculator handles both by splitting the dataset into lower and upper halves around the median.
Why ignore text?
Statistical summaries should only use valid numbers, so non-numeric entries are skipped.
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