FACTOID # 17: Though Rhode Island is the smallest state in total area, it has the longest official name: The State of Rhode Island and Providence Plantations.
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Encyclopedia > Qualitative variation

Qualitative variation (QV) allows us to assess the degree of statistical dispersion in nominal distributions. In descriptive statistics, statistical dispersion (also called statistical variability) is quantifiable variation of measurements of differing members of a population within the scale on which they are measured. ...

Variance is minimized if all cases belong to a single category and is maximized when all cases are qually distributed across all categories. The lower bound of qualitative variation is 0 - when all cases belong to a single category.

The larger the number of categories and the laeger the differences in frequencies across categories, the larger the variance.

Index of qualitative variation (IQV) is defined as a ratio of observed differences to maximum differences.

See also

In probability theory and statistics, the variance of a random variable (or somewhat more precisely, of a probability distribution) is a measure of its statistical dispersion, indicating how its possible values are spread around the expected value. ...

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