Five Number Summary & Outlier Calculator
Build a five-number summary with a stated median-of-halves quartile method, then apply the common 1.5×IQR outlier rule.
Turn quartiles into explicit box-plot fences and whiskers
After calculating Q1 and Q3 with the stated median-of-halves convention, Lynara applies the common 1.5×IQR rule to show lower and upper fences. Values outside those fences are listed as potential outliers, while the furthest in-range observations become the whisker endpoints.
An outlier flag is a descriptive rule, not a verdict that the observation is wrong. Keep unusual values unless the assignment or data-cleaning method gives a defensible reason to remove them, and remember that other software can use a different quartile convention.
Privacy: calculator inputs are processed in your browser; Lynara does not need to upload these values to calculate the result.
Formula
IQR = Q3 − Q1; lower fence = Q1 − 1.5×IQR; upper fence = Q3 + 1.5×IQR
Example
For 1, 2, 3, 4, 5, 100 the median-of-halves method gives Q1 = 2 and Q3 = 5, flags 100 above the 9.5 upper fence, and leaves 5 as the upper whisker.
Useful for
- Box-plot preparation
- Outlier checks with 1.5×IQR
- Descriptive statistics
- Quartile homework
Questions
Why can quartiles differ from another calculator?
There are several valid quartile conventions. This tool states and consistently uses the median-of-halves method.
How are outliers flagged?
Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are listed as outliers; the nearest in-range observations are reported as whiskers.