Categorical and Quantitative Variables

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Categorical vs. Quantitative
Variables

Identifying the Difference
Variables Come in 2 Varieties

1.   Categorical (or __________)

2. Quantitative (or __________)

Introduction to Statistics--   2
Variables
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)
Introduction to Statistics--   3
Variables
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
Introduction to Statistics--   4
Variables
2 Types of Quantitative Variables

1. __________ 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) Usually a variable
that can be ‘counted’.
2.   __________   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’.

Introduction to Statistics--              5
Variables
Diagram of Variable Types
Categorical
(Qualitative)

Variables                            Discrete

Quantitative
(Numerical)

Continuous

Introduction to Statistics--         6
Variables
Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete? Units?
1) Length of a pen?                        Subject of a book?
2) Type of pen?                            Number of pages in the
book?
3) Number of pens in                       Area of each page of
box?                                     book?
4) Maker of pen?                           Number of letters on a
5) Flow of ink in ml/sec?                   page?
6) Color of pen’s ink?                     Number of weeks on
7) Point size of pen?                       best seller list?

Introduction to Statistics--                    7
Variables
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?

Introduction to Statistics--   8
Variables
Reviewing Variable Types

1.    __________ (or __________)

2. __________ (or __________)

Introduction to Statistics--   9
Variables
Reviewing ________ Variables

• Possible responses are ________ in nature
• Includes values for which it makes sense to do
operations like ________, ________ and
________.
questions
• Includes ‘________’
• Usually—best illustrated with a ________, but
___________________________________.

Introduction to Statistics--   10
Variables
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)

Introduction to Statistics--   11
Variables
Classwork & Homework

• Use the terms you’ve learned to analyze
the types of variables you encounter in the
samples
the nature of this survey using the data

Introduction to Statistics--   12
Variables

Introduction to Statistics--   13
Variables
Finding Individuals & Variables
in a List
State          Region           Population             Males     Females
Alabama        South            15.6m                  8.3m      7.2m
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           Variable = Region    = Categorical
Who’s in Sample?                  Variable = Population = Discrete Quantitative
Alabama, Alaska, Arizona        Variable = Males =      Discrete Quantitative
Variable = Females = Discrete Quantitative

Look for Variable Names in Column Headings

Introduction to Statistics--                    14
Variables
Variables Come in 2 Varieties

1.   Categorical (or Qualitative)

2. Quantitative (or Numerical)

Introduction to Statistics--   15
Variables
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).

Introduction to Statistics--   16
Variables
Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?
1) Length of a pen?                  Quantitative, Continuous
2) Type of pen?                      Categorical

3) Number of pens in
Quantitative, Discrete
box?
4) Maker of pen?
Categorical
5) Flow of ink in ml/sec?
Quantitative, Continuous
6) Color of pen’s ink?
Categorical

Introduction to Statistics--               17
Variables
Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?

   Subject of a book?             Categorical
   Number of pages in the         Quantitative, Discrete
book?
   Area of each page of
book?                          Quantitative, Continuous
   Number of letters on a         Quantitaitve, Discrete
page?
   Number of weeks on
best seller list?              Quantitative, Discrete

Introduction to Statistics--             18
Variables
Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?
1) Style of pants?                   Categorical
2) Color of pants?                   Categorical
3) Number of pairs of
pants you own?                    Quantitative, Discrete
4) # of pockets on pants?            Quantitative, Discrete
5) Size of pants?                    Quantitative, Discrete
Categorical
6) Maker of the pants?
7) Length of inseam on the
pants?                            Quantitative, Continuous

Introduction to Statistics--               19
Variables
Reviewing Variable Types

1.   Categorical (or Qualitative)

2. Quantitative (or Numerical)

Introduction to Statistics--   20
Variables
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.

Introduction to Statistics--   21
Variables
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.

Introduction to Statistics--   22
Variables
2 Types of Quantitative Variables
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).

2. 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)

Introduction to Statistics--            23
Variables

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