Part I. Ways to Describe Data

Investigations 1-3: Categorical/Numerical Data & Nominal/Ordinal Data

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.

Table 1. Distribution of Yellow and Red M&Ms
bag id year of
weight in
type of
# yellow
% red
(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.