IQR Calculator
Calculate the interquartile range (IQR) from any dataset. Find Q1, Q3, IQR, fences, and detect outliers automatically.
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📖 How to Use
Step 1: Enter your numbers separated by commas or spaces. Click "Example" for a demo dataset.
Step 2: Click "Calculate" for instant results with box plot and interpretation.
Step 3: Use "Copy" or "CSV" to export results. Click "Recalculate" to try new data.
What Is IQR?
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of a dataset, making it a robust measure of variability that is resistant to outliers. Formula: IQR = Q3 − Q1.
How to Calculate IQR
Sort your data from smallest to largest. Find Q1 (the median of the lower half) and Q3 (the median of the upper half). Subtract Q1 from Q3 to get the IQR. This calculator performs all these steps automatically and also computes the outlier fences.
IQR and Outlier Detection
The IQR is the foundation of the 1.5×IQR rule for detecting outliers. The lower fence is Q1 − 1.5×IQR, and the upper fence is Q3 + 1.5×IQR. Any data point outside these fences is flagged as a potential outlier. This method is used in box plots and is the standard approach in most statistics courses.
IQR vs Range
The range (Maximum − Minimum) measures total spread but is extremely sensitive to outliers. The IQR measures only the central 50% and is unaffected by extreme values. For skewed or outlier-heavy data, the IQR provides a more reliable measure of typical variability.
IQR vs Standard Deviation
Both measure spread, but they differ in sensitivity. Standard deviation uses every data point and is pulled by outliers. IQR uses only Q1 and Q3 and ignores extremes. For normally distributed data, IQR ≈ 1.35 × SD. When data is not normal, the IQR is generally more informative.
❓ Frequently Asked Questions
What does IQR stand for?
IQR stands for Interquartile Range. It is the difference between the third quartile (Q3) and the first quartile (Q1), representing the spread of the middle 50% of data.
How is IQR used to find outliers?
Using the 1.5×IQR rule: values below Q1 − 1.5×IQR (lower fence) or above Q3 + 1.5×IQR (upper fence) are potential outliers.
Is a higher IQR good or bad?
Neither — it depends on context. A higher IQR means more variability in the central data. In quality control, lower IQR indicates more consistent results.
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