Section 1-2
Variables and types of Data
Objective 3: Identify types of
Data
•
In this section we will detail the types
of data and nature of variables.
1-2 Variables and Types of
Data
Data
Qualitative
Categorical
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Quantitative
Numerical,
Can be ranked
Discrete
Continuous
Countable
5, 29, 8000, etc.
Can be decimals
2.59, 312.1, etc.
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Data
Qualitative
Quantitative
Discrete
Continuous
Qualitative variables
•
Are variables that can be placed into
distinct categories, according to some
characteristic or attribute such as:
 Gender
 Political affiliation
 Grade level
Quantitative variables
•
Are numerical and can be ordered or
ranked. For example:
 Age
 height
 weight
Discrete variables
•
Assumes values that can be counted.
For example:
 Number of coffee shops in NoPo.
 Number of turkeys your mama is going
to cook on Thanksgiving.
 Number of unwanted hair on your
chin.
Continuous variables
•
Result from a measurement and can
take on infinite number of values,
including decimal. For example:
 Temperature of a fully cooked turkey..
 Weigh of a turkey
 Ounces of gravy on mashed potatoes.
Rounding
•
•
•
Continuous data is rounded.
Continuous data is usually rounded to
the nearest given unit.
Raw data and boundaries
1-2 Recorded Values and
Boundaries
Variable
Length
Recorded Value
15 centimeters
(cm)
Temperature 86 Fahrenheit
(F)
Time
0.43 second
(sec)
Mass
1.6 grams (g)
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Boundaries
14.5-15.5 cm
85.5-86.5 F
0.425-0.435
sec
1.55-1.65 g
About Boundaries
•
•
•
Boundaries always have one more
decimal place than the data.
Boundaries always end in a 5.
We will cover boundaries further in
chapter 2.
Examples
Page 8
Levels of measure
Nominal
Interval
Ordinal
Ratio
Nominal – categorical (names)

When measuring using a nominal scale, one simply
names or categorizes responses. Gender, handedness,
favorite color, and religion are examples of variables
measured on a nominal scale.

The essential point about nominal scales is that they do
not imply any ordering among the responses. For
example, when classifying people according to their
favorite color, there is no sense in which green is placed
"ahead of" blue.

Responses are merely categorized. Nominal scales
embody the lowest level of measurement.
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Ordinal – nominal, plus can be
ranked (order)

A researcher wishing to measure consumers' satisfaction with their
microwave ovens might ask them to specify their feelings as either
"very dissatisfied," "somewhat dissatisfied," "somewhat satisfied,"
or "very satisfied." The items in this scale are ordered, ranging
from least to most.

This is what distinguishes ordinal from nominal scales. Unlike
nominal scales, ordinal scales allow comparisons, ranking or
“ordering”
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Interval – ordinal, plus intervals are
consistent
Interval scales are numerical scales in which
intervals have the same interpretation
throughout.
Interval scales are not perfect, however. In
particular, they do not have a true zero point
even if one of the scaled values happens to
carry the name "zero."
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Ratio – interval, plus ratios are
consistent, true zero

The ratio scale of measurement is the most informative scale. It is
an interval scale with the additional property that its zero position
indicates the absence of the quantity being measured.

You can think of a ratio scale as the three earlier scales rolled up in
one. Like a nominal scale, it provides a name or category for each
object (the numbers serve as labels). Like an ordinal scale, the
objects are ordered (in terms of the ordering of the numbers). Like
an interval scale, the same difference at two places on the scale
has the same meaning. And in addition, the same ratio at two
places on the scale also carries the same meaning.
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Consequences of level of
measurement
Why are we so interested in the type of
scale that measures a dependent variable?
The crux of the matter is the relationship
between the variable's level of measurement
and the statistics that can be meaningfully
computed with that variable.
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

Let's practice
The website above also some more
examples and explanation of what we just
covered.
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1-2 Variables and Types of Data
Determine the measurement level.
Variable
Nominal Ordinal Interval
Ratio Level
Hair Color
Yes
No
Nominal
Zip Code
Yes
No
Nominal
Letter Grade
Yes
Yes
No
ACT Score
Yes
Yes
Yes
No
Interval
Height
Yes
Yes
Yes
Yes
Ratio
Age
Yes
Yes
Yes
Yes
Ratio
Temperature (F)
Yes
Yes
Yes
No
Interval
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Ordinal
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On your own

Study the examples
listed on table 1-2 on
page 8.


Do applying concepts
on page 9
And answer questions
1-10 on page 26.
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