Find the quartiles, interquartile range, and Tukey fences for spotting potential outliers.
| Q1 | – |
| Q2 (median) | – |
| Q3 | – |
| IQR | – |
| Lower fence | – |
| Upper fence | – |
Use this calculator to summarise the middle of a numeric list and to mark Tukey-style fences. Quartiles split the sorted values into four parts; the interquartile range (IQR) is the width of the middle 50%. Points below the lower fence or above the upper fence are conventional outlier flags, not automatic errors.
Q1, Q2, and Q3 are the 25th, 50th, and 75th percentiles using linear interpolation on the sorted list. IQR = Q3 − Q1. The fences are Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. The default list 1 through 9 plus 20 has a high fence that flags 20.
You need at least four numbers. Other quartile rules (for example exclusive medians) can differ by a small amount. Fences are a plotting convention, not a hypothesis test.
Values: Numbers separated by commas, spaces, or semicolons.
Q1 / Q2 / Q3: First quartile, median, and third quartile.
IQR: Interquartile range, Q3 minus Q1.
Lower fence / Upper fence: Tukey 1.5 × IQR fences.
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