Chapter 1: Section 2-4
Variables and types of Data
Section 2: Types of Variables
Qualitative Variables:
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Variables that can be placed into distinct
categories, according to some
characteristic or attribute.
Ex: Gender, Eye color, Geographic
Location
2 Types of Variables
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Quantitative Variables:
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Variables that are numerical and can be
ordered or ranked.
Ex: Age, height, weight, body temp
Classified by two groups
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Discrete Variables
Continuous Variables
Discrete Variables
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Assume values that can be counted
Assigned numbers such as 0,1,2,3,…
Ex:
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# of children
# of students
Continuous Variables
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Can assume an infinite number of
values between any two specific values.
Obtained by measuring
Often include fractions and decimals.
Ex:
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Temperature
Time
Length
Measurement Scale
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Used to categorize, count, or measure
variables.
Types:
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Nominal
Ordinal
Interval
Ratio
Nominal Level of Measurement
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Classifies data into mutually exclusive,
exhausting categories in which no order
or ranking can be imposed on the data.
Ex:
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Male/Female
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Single/Married/Divorced/Widowed/Separated
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Democratic/Republican
Ordinal Level of Measurement
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Classifies data into categories that can
be ranked; however, precise differences
between the ranks do not exist.
Ex:
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Letter Grades (A, B, C, D, F)
1st, 2nd, 3rd, etc
Small, Medium, Large
Freshman, Sophomores, Juniors, Seniors
Interval Level of Measurement
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Ranks data, and precise differences
between units of measures do exist:
however, there is no meaningful zero.
Ex:
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Temperature: 72°F and 73°F, difference of
1°F, but 0°F does not mean no heat
present
IQ: 109 and 110, difference of 1 point, but
0 does not mean there is no intelligence.
Ratio Level of Measurement
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Possesses all the characteristics of interval
measurements, and there exists a true zero.
In addition, true ratios exists when the same
variables is measured on two different
members of the population.
Ex:
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Salary
Time
Age
Checking for Understanding
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“Applying the Concepts” page 9, # 1-6.
Section 3: Data Collection and
Sampling Techniques.
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Types:
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Random
Systematic
Stratified
Cluster
Random Sampling
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Selection based on chance or random
numbers.
Procedure:
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Assign number to each subject in
population
Select numbers at random from “hat”
Random Sampling
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Systematic Sampling
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Procedure:
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Number each subject in population
Select every kth subject
Example:
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Population: 100 Sample: 10
Kth term: 100/10=10
1, 11, 21, 31, 41, 51, 61, 71, 81, 91
Systematic Sampling
Population: 21 Sample: 7
21/7=3: kth term is 3.
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Stratified Sampling
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Procedures:
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Population divided into groups called:
Strata
Groups have common characteristic
needed for study.
Samples randomly selected from each
strata
Stratified Sampling
Cluster Sampling
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Population is divided into groups called:
Clusters
Select some clusters
Survey every member of the cluster for
sample
Used with large populations
Cluster Sampling
Other sampling methods
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Convenience sampling
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Use subjects that are convent
Ex: asking people as they enter the mall
Sequential sampling
Double sampling
Multistage sampling
Convenience Sampling
Do you want to
take a survey?
Practice
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Page 26-27
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#’s 6, 7, 8, 9, 11, 12
Section 4: 2 Types of Studies
Observational Study
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Researchers merely observe what is
happening or what has happened in the
past
Try to draw conclusions based on these
observations.
Ex: studying creatures in the wild
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“Meerkat Manor”
Section 4: 2 Types of Studies
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Experimental study
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Researchers manipulate one of the
variables
Tries to determine how to the manipulation
influences other variables.
Ex: New medication and placebos
Statistical Studies include….
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Independent variables
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In an experimental study is the one that is
being manipulated by the researcher.
Also called: Explanatory variable
Dependent variables
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Resultant variable
Also called: Outcome variable
Misuses of Statistics
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Suspect Samples
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Too small
Convenience
Volunteers
Changing the subject
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Increase of 3%
Increase of $600,000
Misuses of Statistics
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Detached Statistics- no comparison
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“Works 5 times faster”
“1/3 fewer calories”
Implied Connection
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“Eating fish may help you achieve better in
school”
Misuses of Statistics
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Misleading Graphs- Chapter 2
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Faulty Survey Questions
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“Do you feel there should be a 4 day
school week?”
“Do you feel there should be a 4 day
school week from 4 am to midnight?”
Section 1-6: Computers and
Calculators
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Computer and Calculators GOOD
End of Chapter 1