Median Quartiles IQR Calculator
Computes median, first quartile Q1, third quartile Q3 and interquartile range IQR of a list of numerical values.
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Quartiles and interquartile range (IQR)
Sort the data, then cut it into four equal parts at Q1 = P25, Q2 = median = P50 and Q3 = P75. The interquartile range, IQR = Q3 − Q1, measures how wide the middle 50% is. Run 1,3,5,7,9,11,13,15 through it and you get Q1 = 4, Q2 = 8, Q3 = 12, so IQR = 8. Tukey (1977) gave us the five-number summary (min, Q1, Q2, Q3, max), which is what the boxplot draws. His rule treats a value as an outlier if it falls below Q1 − 1.5·IQR or rises above Q3 + 1.5·IQR; for extreme outliers the multiplier becomes 3·IQR.
Applications
You'll see them in boxplots during exploratory analysis, in SRE latency reports with P50/P95/P99 SLAs, in salary surveys, and across robust statistics, where the IQR shrugs off outliers in a way the standard deviation can't. They're handy in quality control too, and in any skewed distribution where the mean and standard deviation paint a misleading picture.
FAQ
Why use IQR instead of range? The range (max − min) is at the mercy of the extremes. Because the IQR throws out the bottom 25% and top 25%, one stray outlier won't budge it.
Why do Excel, R and NumPy give different quartiles? Hyndman & Fan (1996) cataloged at least nine ways to define a quantile. With small n those methods pull apart; as n grows they settle on the same answer.
Is the 1.5·IQR rule a hard cutoff? No, it's just a rule of thumb. On a normal distribution it tags about 0.7% of points as outliers. Look at whatever it flags before you throw anything out.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.