Five-Number Summary Calculator
Get the five-number summary — minimum, Q1, median, Q3 and maximum — plus the interquartile range and outlier fences for any data set.
How it works
IQR = Q3 − Q1 · Outlier fences = Q1 − 1.5 × IQR and Q3 + 1.5 × IQR
The five-number summary compresses a data set into its minimum, first quartile (Q1), median, third quartile (Q3) and maximum — the same five values a box plot draws. The middle 50% of the data spans the interquartile range, Q3 minus Q1. Tukey’s 1.5 × IQR rule then sets fences beyond the quartiles, and any point past a fence is flagged as a potential outlier worth a closer look.
Worked example
For 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 the summary is minimum 7, Q1 36, median 40.5, Q3 43, maximum 49. The IQR is 7, so the fences sit at 36 − 10.5 = 25.5 and 43 + 10.5 = 53.5 — flagging 7 and 15 as low outliers.
Frequently asked questions
How are the quartiles calculated here?
The data is split at the median; Q1 is the median of the lower half and Q3 the median of the upper half. With an odd number of values the median itself is excluded from both halves (Tukey’s method), so answers may differ slightly from a spreadsheet using another convention.
Why 1.5 times the IQR for outliers?
It is a convention introduced by John Tukey that balances catching genuine outliers against false alarms. Some analyses use 3 × IQR for "far out" extreme values, but 1.5 is the standard for the whiskers on a box plot.
Is a flagged outlier automatically bad data?
Not at all. The fences only mark points worth investigating. An outlier can be a data-entry error, or it can be the most interesting real observation in the set — decide only after looking at why it is extreme.
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