Key takeaway: An outlier is a data value that lies far from the other values in a set, and it can pull the mean toward itself while the median stays almost unchanged.
Grade 66.SP.B.5dStatistics and Data
Definition of Outlier
An outlier is a value that stands apart from the pattern of the rest of the data. On a dot plot it appears as a lone dot far from the main cluster; on a number line there is a large empty gap before it.
It may come from a mistake in recording, an unusual event, or a real but rare case. Do not delete it automatically. First check whether it is an error, then decide whether it belongs in the analysis. An outlier changes measures that use every value, such as the mean and the range, much more than measures based on position, such as the median and the interquartile range.
Formula and notation
There is no symbol for it. In grade 6 you recognize it by a visual gap and by how it shifts a summary:
\[\text{mean with outlier} \ne \text{mean without outlier}\]
Report both versions when an unusual value is present, and say which measure of center you trust more.
Key facts
- It can raise or lower the mean noticeably but moves the median very little.
- Looking at a dot plot or box plot is the quickest way to find one.
- A suspicious value should be checked for a recording error before it is removed.
- It is a feature of the data set, not a mistake by definition.
Outlier example
A school bus was late by 14, 15, 16, 16, 17, 18 and 52 minutes on seven days. Identify the outlier and compare the mean and median with and without it.
-
Six values lie between 14 and 18, and 52 is far away, so 52 is the outlier.
-
Without it: mean \(= \frac{96}{6} = 16\), median \(= 16\).
-
With it: the total is \(96 + 52 = 148\), so the mean is \(\frac{148}{7} \approx 21.1\), while the median is still 16.
The outlier is 52. It raises the mean from 16 to about 21.1 and leaves the median at 16.
Common mistake
Watch out
Remy sees 52 and crosses it out immediately because “it ruins the data.”
Why it is wrong
Unusual does not mean wrong. Maybe the bus broke down that day, which is real information. Check the source, then decide, and report the summary both ways so readers see the effect.
Related terms and lessons
- Grade 6 · Mean, Median, Range, IQR and Mean Absolute DeviationLessonWorksheetQuiz
- Algebra 1 · Statistics: Center, Spread and Data DisplaysLessonWorksheetQuiz
Browse the glossary: A–Z list · Grade 6 vocabulary · Statistics and Data