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, letâ€™s consider the data in Table 1.

Table 1. Distribution of Yellow and Red M&Ms

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.