Part I. Ways to Describe Data

Investigations 4 and 5: Ratio/Interval Data & Discrete/Continuous Data

We also can use a numerical variable to assign samples to groups. For example, we can divide the plain M&Ms in Table 1 into two groups based on the sample’s weight. What makes a numerical variable more interesting, however, is that we can use it to make quantitative comparisons between samples; thus, we can report that there are 14.8 times as many plain M&Ms in a 10-oz. bag as there are in a 0.8-oz. bag. Although we can complete meaningful calculations using any numerical variable, the type of calculation we can perform depends on whether or not the variable’s values have an absolute reference.

Investigation 4. A numerical variable is described as either ratio or interval depending on whether it has (ratio) or does not have (interval) an absolute reference. Explain what it means for a variable to have an absolute reference and assign each of the numerical variables in Table 1 as either a ratio variable or an interval variable. Why might this difference be important?

Investigation 5. Numerical variables also are described as discrete or continuous. Define the terms discrete and continuous and assign each of the numerical variables in Table 1 to one of these terms.