Which dispersion measure is the proportion of non-modal values to all values?

• A. Variation ratio
• B. Bar chart
• C. Semi-interquartile range
• D. Histogram

Answer: (A)

The measure in question is the variation ratio. It quantifies dispersion by looking at how many observations do not take the most frequent value (the mode). Specifically, it’s the proportion of non-modal values to the total number of observations, which tells you how spread out the data are around the modal category. For nominal data, where you can count categories but can’t meaningfully compute means or variances, this ratio directly expresses how much the data diverge from the most common category: if everyone is the same, dispersion is zero; if most observations differ from the mode, dispersion is high. The other options aren’t dispersion measures based on this idea: a bar chart or a histogram are visual representations of distribution, and the semi-interquartile range is a measure of spread based on quartiles for numerical data, not the proportion of non-modal values.