The Interquartile Range Calculator finds Q1, Q2 (median), and Q3 from your dataset, then calculates the IQR. It supports four modes: basic IQR calculation, five-number summary, outlier detection using the 1.5 x IQR rule, and box plot data generation.
Enter comma-separated values to see the quartiles, fences, and any outliers. The outlier detection mode classifies values as mild or extreme outliers, and the box plot mode includes an SVG visualisation of your data distribution.
Your calculations will appear here
The interquartile range (IQR) measures the spread of the middle 50% of a dataset. It is calculated as Q3 minus Q1, where Q1 is the 25th percentile and Q3 is the 75th percentile. The IQR is resistant to outliers, making it a robust measure of spread.
The five-number summary consists of the minimum, Q1, median (Q2), Q3, and maximum. It provides a concise description of the distribution of a dataset and forms the basis for box-and-whisker plots.
Outlier detection using the IQR method defines fences: lower fence = Q1 - 1.5 x IQR and upper fence = Q3 + 1.5 x IQR. Values outside these fences are considered outliers. Values beyond Q1 - 3 x IQR or Q3 + 3 x IQR are classified as extreme outliers.
Box plots (box-and-whisker diagrams) visualise the distribution of data using the five-number summary. The box spans Q1 to Q3, a line marks the median, and whiskers extend to the most extreme non-outlier values. Outliers are plotted as individual points beyond the whiskers.
Problem: Find the IQR of: 2, 4, 7, 8, 10, 12, 15.
Solution: Sorted: 2, 4, 7, 8, 10, 12, 15. Q1 = median of {2, 4, 7} = 4. Q3 = median of {10, 12, 15} = 12. IQR = 12 - 4 = 8.
Answer: IQR = 8
Problem: Detect outliers in: 2, 4, 7, 8, 10, 12, 15, 50.
Solution: Q1 = 5.5, Q3 = 13.5, IQR = 8. Lower fence = 5.5 - 12 = -6.5. Upper fence = 13.5 + 12 = 25.5. 50 > 25.5, so 50 is an outlier.
Answer: Outlier: 50
Problem: Find the five-number summary of: 3, 7, 8, 5, 12, 14, 21, 13, 18.
Solution: Sorted: 3, 5, 7, 8, 12, 13, 14, 18, 21. Min = 3, Q1 = 6, Median = 12, Q3 = 16, Max = 21.
Answer: {3, 6, 12, 16, 21}
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