Outlier
In short: Outlier is a data value that sits far away from the rest of the values, such as one huge number in an otherwise tightly grouped list.
6th GradeStatistics6.SP.B.5d
What is Outlier?
An outlier is the lone dot way off to one side of a graph. It might be a rare event, a typing mistake or a truly unusual case, and it deserves a second look before you summarize the data.
Such a value pulls the mean toward itself and stretches the range, but it barely moves the median. That is why the median is often a better description of a typical value when an outlier is present.
How to spot it
- A dot plot or box plot shows a single value separated from the others by a big gap.
- A list is mostly close together, but one entry is several times larger or smaller than the rest.
- The mean and median of a data set are far apart.
- A reported measurement looks impossible, such as a student height of 600 inches.
The method
- Sort the data and look for a value separated from the rest by a clear gap.
- Check whether it is a mistake; if it is, fix it, and if it is real, keep it and note it.
- Compute the mean and median with and without it.
- Report the median when it changes much less than the mean.
Outlier: solved example
Problem
A cyclist in Boulder logs ride times of 10, 11, 12, 13, 14 and 60 minutes. Spot the far-off value and compare the mean and median with and without it.
Solution
The value 60 is far from the others, so it is the unusual one. With it: mean \(\frac{120}{6} = 20\) and median \(\frac{12 + 13}{2} = 12.5\).
Without it: mean \(\frac{60}{5} = 12\) and median 12. The mean changed by 8 while the median changed by 0.5, so the median is the better typical value.
Try it
Question 1
In the list 4, 5, 5, 6, 7, 41, which value is far off, and what is the median?
Show the answer
41 is far from the rest. The median is \(\frac{5 + 6}{2} = 5.5\).
Question 2
True or false: removing such a value always lowers the mean.
Show the answer
False. Removing a very low one raises the mean.
Outlier vs. Range
The range is a number: the gap between the largest and smallest values. An outlier is one of the values itself, a point that sits unusually far from the rest. An outlier makes the range large, but a large range does not require one.
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Whole dictionary: A–Z · 6th Grade · Statistics