Question

Describe the relation between scales of measurement and measures of variability (e.g., interquartile range and standard deviation.)

Answer 1

When dealing with nominal scales we have the same limitations we had with measures of central tendency. Numbers assigned to nominal scales are not truly numbers – they are name labels. We, therefore, cannot calculate a number that would describe the variability of the responses.   In fact, we cannot even meaningfully say that the scores range from category 1 to category 7 because the order of the categories is arbitrary.  

With ordinal scales, we can define the Range of the categories. We might say our sample included respondents ranging in education level from no high school through to PhDs. This defines the extremes or endpoints of our ordered categories. Since the intervals are not equal between our categories, we cannot define in numbers the average difference between scores.

With continuous /scale variables, (Interval and Ratio) we can use numbers to describe the variability of the distribution.

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