Categorical vs. Quantitative
Variables
Identifying the Difference
Variables Come in 2 Varieties
1.
Categorical (or __________)
2. Quantitative (or __________)
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Categorical Variable Characteristics
• Recorded usually with words
• Records which of several groups an
individual belongs to
• Count data in each group, but you
logically should not average it
• Can calculate %age distributions
• Includes all yes/no questions
• Graphing: best illustrated with a pie chart
(but could also be a bar graph)
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Quantitative Variable Characteristics
• Possible responses are numerical in
nature
• Includes values for which it makes sense
to do operations like adding, totaling and
averaging
• Includes answers to how much/how
many questions
• Always includes ‘units’
• Graphing: best illustrated with a bar chart
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2 Types of Quantitative Variables
1. __________ If the Q variable is a set
2.
__________
of isolated points on the
number line, we call it this.
(i.e., it’s a number but it only comes
in certain values) Usually a variable
that can be ‘counted’.
If the Q variable forms an entire
interval along the number line, we
call it this. (i.e., it’s a number & it can be
any value) Usually a variable that can
be ‘measured’.
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Diagram of Variable Types
Categorical
(Qualitative)
Discrete
Variables
Quantitative
(Numerical)
Continuous
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Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete? Units?
1) Length of a pen?
2) Type of pen?
3) Number of pens in
box?
4) Maker of pen?
5) Flow of ink in ml/sec?
6) Color of pen’s ink?
7) Point size of pen?
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
Subject of a book?
Number of pages in the
book?
Area of each page of
book?
Number of letters on a
page?
Number of weeks on
best seller list?
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Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete? Units?
1) Style of pants?
2) Color of pants?
3) Number of pairs of
pants you own?
4) # of pockets on pants?
5) Size of pants?
6) Maker of the pants?
7) Length of inseam on the
pants?
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Reviewing Variable Types
1.
__________ (or __________)
2. __________ (or __________)
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Reviewing ________ Variables
• Possible responses are ________ in nature
• Includes values for which it makes sense to do
operations like ________, ________ and
________.
• Includes answers to ________/________
questions
• Includes ‘________’
• Usually—best illustrated with a ________, but
___________________________________.
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2 Types of __________ Variables
1. __________ If the Q variable forms an entire
interval _______________, we
call it this.
(i.e., it’s a number & it can be any
value).
2. __________ If the Q variable is a set
of isolated ___________
_________, we call it this.
(i.e., it’s a number but it only comes
in certain values)
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Classwork & Homework
• Use the terms you’ve learned to analyze
the types of variables you encounter in the
samples
• Answer some the ‘usual’ questions about
the nature of this survey using the data
and your powers of analysis.
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Answers to Fill in Blanks
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Finding Individuals & Variables
in a List
State
Region
Population
Males
Females
Alabama
Alaska
South
West
15.6m
5.4m
8.3m
2.5m
7.2m
2.9m
Arizona
West
10.2m
5.1m
5.1m
Individuals in Sample—Usually in 1st Column
Variables—Usually in 2nd and succeeding columns
Number of in Sample = 3
Who’s in Sample?
Alabama, Alaska, Arizona
Variable = Region
= Categorical
Variable = Population = Discrete Quantitative
Variable = Males =
Discrete Quantitative
Variable = Females = Discrete Quantitative
Look for Variable Names in Column Headings
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Variables Come in 2 Varieties
1.
Categorical (or Qualitative)
2. Quantitative (or Numerical)
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2 Types of Quantitative Variables
1. Discrete
If the Q variable is a set
of isolated points on the
number line, we call it this.
(i.e., it’s a number but it only comes
in certain values)
2. Continuous If the Q variable forms an entire
interval along the number line, we
call it this.
(i.e., it’s a number & it can be any
value).
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Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?
1) Length of a pen?
2) Type of pen?
3) Number of pens in
box?
4) Maker of pen?
5) Flow of ink in ml/sec?
6) Color of pen’s ink?
Quantitative, Continuous
Categorical
Quantitative, Discrete
Categorical
Quantitative, Continuous
Categorical
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Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?





Subject of a book?
Number of pages in the
book?
Area of each page of
book?
Number of letters on a
page?
Number of weeks on
best seller list?
Categorical
Quantitative, Discrete
Quantitative, Continuous
Quantitaitve, Discrete
Quantitative, Discrete
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Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?
Categorical
Categorical
1) Style of pants?
2) Color of pants?
3) Number of pairs of
pants you own?
4) # of pockets on pants?
5) Size of pants?
6) Maker of the pants?
7) Length of inseam on the
pants?
Quantitative, Discrete
Quantitative, Discrete
Quantitative, Discrete
Categorical
Quantitative, Continuous
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Reviewing Variable Types
1.
Categorical (or Qualitative)
2. Quantitative (or Numerical)
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Reviewing Quantitative Variables
• Possible responses are numerical in nature
• Includes values for which it makes sense to do
operations like adding, totaling and averaging.
• Includes answers to how much/how many
questions
• Includes ‘units’
• Usually—best illustrated with a bar graph, but
pie chart is also possible.
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•
•
•
•
•
•
Reviewing Categorical Variables
Recorded usually with words
Records which of several categories an
individual belongs to
Count data in each group, but you
logically should not average it
Can calculate percentage distributions
Includes all yes/no questions
Usually—best illustrated with a pie chart.
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2 Types of Quantitative Variables
2.
Continuous
2. Discrete
If the Q variable forms an entire
interval along the number line, we
call it this.
(i.e., it’s a number & it can be any
value).
If the Q variable is a set
of isolated points on the
number line, we call it this.
(i.e., it’s a number but it only comes
in certain values)
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