Practical guide and verification
State the quartile convention with the result
Q1 and Q3 are not defined identically by every textbook or statistics package. Small datasets can therefore produce different quartiles under different interpolation or median-inclusion conventions even when every implementation is internally correct.
Sort and inspect the data before interpretation
Quartiles describe an ordered sample. Check for accidental duplicates, pasted labels, wrong units, and transcription errors before relying on the five-number summary or box plot. A single bad value can move the IQR and outlier fences.
Use IQR as a spread measure, not an automatic deletion rule
The interquartile range summarizes the middle half of the observations. Values beyond a chosen IQR fence are candidates for review, not automatically mistakes. Real extreme observations can be scientifically or operationally important.
Compare methods when a small sample is sensitive
If two quartile conventions materially change the conclusion, report the convention or compare both. The method-comparison panel is especially useful for classroom work and for reproducing results from software that uses a different default.
Verify the median and fence arithmetic independently
The median should split the ordered data around the center according to the selected convention. Check IQR as Q3 minus Q1, then confirm lower and upper fences as Q1 minus k×IQR and Q3 plus k×IQR.
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