Find outliers with the 1.5 × IQR rule — fences, quartiles and box plot
Enter your numbers to detect outliers using the standard 1.5 × IQR rule. The calculator also shows the upper and lower fences, the quartiles and a box plot marking each outlier.
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An outlier is a value that lies an unusual distance from the rest of the data. Outliers can be genuine extreme observations or the result of measurement and data-entry errors, so spotting them is an important first step before any further analysis.
The most common definition is based on the interquartile range. First find Q1, Q3 and IQR = Q3 − Q1. The inner "fences" sit at Q1 − 1.5 × IQR and Q3 + 1.5 × IQR; any value beyond them is flagged as a potential outlier. The outer fences sit at 3 × IQR beyond the quartiles, and values past those are considered extreme outliers. This calculator reports both fences and lists every value that falls outside them.
Not automatically. An outlier flag is a prompt to investigate, not a licence to delete data. If a value is a clear error, correcting or removing it is reasonable; if it is a real observation, it may be the most interesting point in the data set. When you do report results with outliers removed, say so explicitly, because robust measures such as the median and IQR are often a better response than deletion.
Compute the IQR (Q3 − Q1). Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is a potential outlier; values beyond 3 × IQR are extreme outliers.
The fences are the thresholds that define outliers. The inner fences are 1.5 × IQR beyond Q1 and Q3; the outer fences are 3 × IQR beyond them. Both are shown in the results above.
No. Investigate first. Remove a value only if it is a genuine error; otherwise consider keeping it and using outlier-resistant measures such as the median and IQR.