# What summary statistics to use with categorical or qualitative variables?

Just to clarify, when I mean summary statistics, I refer to the Mean, Median Quartile ranges, Variance, Standard Deviation.

When summarising a univariate which is categorical or qualitative, considering both Nominal and Ordinal cases, does it make sense to find its mean, median, quartile ranges, variance, and standard deviation?

If so is it different than if you were summarising a continuous variable, and how?

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I barely see any difference between categorical and qualitative variable, except one of terminology. Anyway, that would be very difficult to compute anything like mean or SD on a nominal variable (e.g., hair color). Maybe you are thinking of categorical variables with ordered levels? –  chl Jul 23 '12 at 7:57
Nope, if the categorical data has an order or ranked levels they are said to be Ordinal according to this website: [stats.gla.ac.uk/steps/glossary/presenting_data.html#orddat], and it says "You can count and order, but not measure, ordinal data" –  chutsu Jul 23 '12 at 9:02
But am I wrong? –  chutsu Jul 23 '12 at 12:44

In general, the answer is no. However, one could argue that you can take the median of ordinal data, but you will, of course, have a category as the median, not a number. The median divides the data equally: Half above, half below. Ordinal data depends only on order.

Further, in some cases, the ordinality can be made into rough interval level data. This is true when the ordinal data are grouped (e.g. questions about income are often asked this way). In this case, you can find a precise median, and you may be able to approximate the other values, especially if the lower and upper bounds are specified: You can assume some distribution (e.g. uniform) within each category. Another case of ordinal data that can be made interval is when the levels are given numeric equivalents. For example: Never (0%), sometimes (10-30%), about half the time (50%) and so on.

To (once again) quote David Cox:

There are no routine statistical questions, only questionable statistical routines

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You provide good related information but I think in response to chl question, the OP made it clear that he is talking about categorical data that is not ordinal. So your response is really not an answwer but I am not one who would give a downvote. But I do think you should change it to a comment. –  Michael Chernick Jul 23 '12 at 11:34
No, I won't downvote the answer as I do think it has added some value to my limited understanding. I should have made it clear in my description that I am considering both Ordinal and Nominal Summary statistics, so the fault is mine. –  chutsu Jul 23 '12 at 12:41