There are no measures of variability for nominal data.

Question

BlackTom AI · Accepted Answer

Consider the statement: 'There are no measures of variability for nominal data.'

First, think about what nominal data entail: categories without a natural order. This means you can’t compute basic spread like a range or standard deviation in the usual sense. However, variability in nominal data can be assessed through the distribution of cases across categories, not by numerical spread.

One way to gauge variability is to examine how evenly the categories are represented. If all categories occur with similar frequencies, the data are highly variable across categories; if one category dominates, variability is low. Measures that capture this concept include the Index of Qualitative Variation (IQV) and Shannon entropy, both designed for nominal data. These indices quantify how dispersed or diverse the category membership is.

Additionally, you can use simple descriptive statistics like the number of distinct categories present (the richness) and the proportions in each category to describe variability. Even though you cannot compute variance or standard deviation for purely nominal data, you still have meaningful dispersion measures that reflect how spread out the data are across categories.

Therefore, the claim is incorrect because there are established measures of variability appropriate for nominal data, even if they differ from those used with ordinal or interval data.

In summary, nominal data do admit concepts of dispersion or variability via category distribution, diversity indices, and entropy, rather than possessing no variability measures at all.

4448_UAC_1064 Quiz 3

There are no measures of variability for nominal data.

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