difficulty 2/5
Outliers
Values far from the rest, which may be mistakes or may be the finding. Detecting them with a mean and a standard deviation fails in a specific way — the more of them there are, the fewer you find.
Intuition
"An outlier is an observation that appears to deviate markedly from other observations in the sample" [1, §1.3.5.17]. That definition does something useful by being careful: it says appears to deviate, and stops. It does not say the value is wrong.
Think Stats puts the ambiguity where it belongs. Outliers are "extreme values that might be errors in measurement and recording, or might be accurate reports of rare events" [2, §2.5], and in its pregnancy-length data all three cases are present at once: lengths "below 10 weeks are certainly errors", values above 30 weeks "are probably legitimate", and in between "it is hard to be sure; some values are probably errors, but some represent premature babies" [2, §2.5].
So the detection question and the handling question are separate, and only the first one is statistical.
Formal definition
How it works
Where it's used
Why & when
Worked example
Pitfalls
Check yourself
3 questions
The questions on this page come with access. They are graded on the server, so the answers stay there until you have given yours.
On the cheat sheet: Missing data and outliers →
Sources
- NIST/SEMATECH e-Handbook of Statistical Methodsstandard · retrieved 2026-09-13https://www.itl.nist.gov/div898/handbook/eda/section3/eda35h.htm
- Think Stats, 2nd ed.book · retrieved 2026-09-13https://greenteapress.com/thinkstats2/html/index.html
- e-Handbook of Statistical Methods — 4.1.4.1 Linear Least Squares Regressionstandard · retrieved 2026-10-04https://www.itl.nist.gov/div898/handbook/pmd/section1/pmd141.htm
- scikit-learn User Guide — Novelty and Outlier Detectiondocs · retrieved 2026-10-04https://scikit-learn.org/stable/modules/outlier_detection.html