Comparing Distributions and Outliers
I can test for outliers with the 1.5 × IQR rule and compare two data sets by center and spread.
What students learn
Students learn to find the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR, decide which values are outliers, see what an outlier does to the mean and the median, and compare two data sets with a fitting center and spread.
See inside
The key rule
A value is an outlier when it is more than 1.5 × IQR below Q1 or above Q3. It is unusual, not automatically wrong.
fences: Q1 − 1.5 × IQR and Q3 + 1.5 × IQR
With an outlier or a skewed shape, the median and IQR usually compare better; for symmetric data, the mean and standard deviation.
Watch out
Rainfall on 9 days, in mm: 2, 3, 3, 4, 5, 5, 6, 7, 48. A real storm gave the 48, an outlier. A student deletes it as a mistake.
The mistake: delete 48: it must be a mistakeUnusual is not the same as wrong.
The fix: keep 48; the median is 5It is real data, and the median barely feels it.
The mistakes it targets
- Deletes a real outlier as a mistake
- Leaves the 1.5 out of the fence formula
- Compares means when one data set has an outlier
- Reverses which way a long tail pulls the mean
- Calls a value an outlier because it is far from its neighbor
- Judges spread by the median and range alone
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 9 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, six common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
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.