Comparing Distributions and Outliers
I can test a value against the 1.5 times IQR rule and compare two data sets by centre, spread and shape.
The problem this sheet solves
The rule says a value is UNUSUAL and says nothing about why. A mistyped entry should go; a student who really scored 105 out of 110 is the most interesting person in the room. Students also decide by eye, and the biggest visible gap is not the test — the rule measures the distance to the QUARTILE, in IQRs, not the distance to the next value. One practice item is built so the eye-catching gap and the actual outlier sit at OPPOSITE ENDS of the same data set, so a gap-hunter is looking at the wrong end. Another has a fence of 43.75, which cannot be estimated off the page at all. The comparison items give two classes with the SAME median and nothing else in common, and the rainfall problem puts the whole question somewhere it matters: a storm drain designed with the storm removed.
The key rule
A value is an outlier when it lies more than 1.5 × IQR beyond a quartile. That makes it unusual, not wrong, and never automatically deletes it.
Count IQRs, not inches.
Watch out
The mistake: Class A's mean is 78 and Class B's is 76.6, so a student says Class A did better.
The fix: Class A's higher mean is one student who scored 105. Both medians are 75.5. A's scores are packed within 4 points; B's spread over 14.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.