Categorical vs. QuantitativeVariables

Identifying the Difference

Introduction to Statistics--Variables

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Variables Come in 2 Varieties

1. Categorical (or __________)

2. Quantitative (or __________)

Introduction to Statistics--Variables

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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)

Introduction to Statistics--Variables

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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 of isolated points on thenumber 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’.

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Diagram of Variable Types

Categorical(Qualitative)

Variables Discrete

Quantitative(Numerical)

Continuous

Introduction to Statistics--Variables

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Categorical or QuantitativeIf 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?

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?

Introduction to Statistics--Variables

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Categorical or QuantitativeIf 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 __________)

Introduction to Statistics--Variables

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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)

Introduction to Statistics--Variables

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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.

Introduction to Statistics--Variables

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Answers to Fill in Blanks

Finding Individuals & Variables in a List

State Region Population Males Females

AlabamaAlaska

SouthWest

15.6m5.4m

8.3m2.5m

7.2m2.9m

Arizona West 10.2m 5.1m 5.1m

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Individuals in Sample—Usually in 1st ColumnVariables—Usually in 2nd and succeeding columns

Number of in Sample = 3Who’s in Sample? Alabama, Alaska, Arizona

Variable = Region = CategoricalVariable = Population = Discrete QuantitativeVariable = Males = Discrete QuantitativeVariable = Females = Discrete Quantitative

Look for Variable Names in Column Headings

Introduction to Statistics--Variables

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Variables Come in 2 Varieties

1. Categorical (or Qualitative)

2. Quantitative (or Numerical)

Introduction to Statistics--Variables

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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. ContinuousIf 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 QuantitativeIf 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 QuantitativeIf 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

Introduction to Statistics--Variables

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Categorical or QuantitativeIf Categorical, one possible category? If Quantitative, Continuous or Discrete?

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?

Categorical

Categorical

Quantitative, Discrete

Quantitative, Discrete

Quantitative, Discrete

Categorical

Quantitative, Continuous

Introduction to Statistics--Variables

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Reviewing Variable Types

1. Categorical (or Qualitative)

2. Quantitative (or Numerical)

Introduction to Statistics--Variables

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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 Variables2. 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 thenumber line, we call it this.

(i.e., it’s a number but it only comes in certain values)