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Just want to make sure that I understand the meaning of an outlier.

Question: Can you have an outlier of categorical data?

I think that to have an outlier you must first have some sort of measurement. My reason is that any data point > 3*IQR (Interquartile range) is used to identifiy an outliner.

However, there is no measurement with categorical data, as I understand.

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up vote 1 down vote accepted

Suppose you have 1000 people choose between apples and oranges. If 999 choose oranges and only one person chooses apple, I would say that that person is an outlier.

We use measurement as a way to detect anomalies. With categorical data you have to explain why choosing an apple is considered an anomaly (that data point does not behave as the rest 99.9% of the population).

There are also papers that talk about outliers in categorical data, for example http://www.cs.umn.edu/tech_reports_upload/tr2008/08-008.pdf.

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I don't know what the standard treatment of this problem is, however I have a remark about the question. In order for the concept outlier to have any meaning you need to be able to define a distance between the values, that in this case may not be trivial i.e. is an apple closer to an orange or a pear?

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That is what I was thinking, but just wanted to make sure that I understood it correctly and wasn't missing something. –  yiyi Oct 23 '12 at 9:00
    
Genetically and morphologically, an apple is closer to a pear than either is to an orange. –  Henry Oct 23 '12 at 9:57

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