In the introduction to this case study we identified four contrasting ways to describe data: categorical vs. numerical, ordered vs. unordered, absolute reference vs. arbitrary reference, and discrete vs. con-tinuous. To give meaning to these descriptive terms, let’s consider the data in Table 1.
| bag id | year of purchase |
weight in ounces |
type of M&M |
# yellow M&Ms |
% red M&Ms |
total M&Ms |
rank (total M&Ms) |
|---|---|---|---|---|---|---|---|
| a | 2006 | 1.74 | peanut | 02 | 27.8 | 018 | sixth |
| b | 2006 | 1.74 | peanut | 03 | 04.3 | 023 | fourth |
| c | 2000 | 0.80 | plain | 01 | 22.7 | 022 | fifth |
| d | 2000 | 0.80 | plain | 05 | 20.8 | 024 | third |
| e | 1994 | 10.0 | plain | 56 | 23.0 | 331 | second |
| f | 1994 | 10.0 | plain | 63 | 21.9 | 333 | first |
Investigation 1. Of the variables included in Table 1, some are categorical and some are numerical. Define these terms and assign each of the variables in Table 1 to one of these terms.
Investigation 2. Suppose we decide to code the type of M&M using 1 for plain and 2 for peanut. Does this change your answer to Investigation 1? Why or why not?
Investigation 3. Categorical variables are described as nominal or ordinal. Define the terms nominal and ordinal and assign each of the categorical variables in Table 1 to one of these terms.