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A nominal variable is where you assign a number to a category. Imagine a variable called "animal" where 1=sheep, 2=cow, 3=dog, etc. Calculating the average, standard deviation or other continuous measures of "animal" in this context wouldn't make any sense. That is, an average "animal" of, say, 4.567 with standard deviation of 1.234 doesn't mean anything.

You could, however, calculate a mode, which is the most frequently occurring category.

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