### Section X.X - DRS & Company

```Section 1.2
Data Classification
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Objectives
o Classify data as qualitative or quantitative; as
discrete, continuous, or neither; and by the level of
measurement.
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Introduction to Statistics
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1.2 Data Classifications
Qualitative vs. Quantitative:
Qualitative
Quantitative
Descriptions and
labels
Counts and
measurements
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Example 1.4: Classifying Data as Qualitative or
Quantitative
Classify the following data as either qualitative or
quantitative.
a. Shades of red paint in a home improvement store
b. Rankings of the most popular paint colors for the
season
c. Amount of red primary dye necessary to make one
gallon of each shade of red paint
d. Numbers of paint choices available at several stores
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Example 1.4: Classifying Data as Qualitative or
Quantitative (cont.)
Solution
a. Shades of paint are descriptions and cannot be
measured, so these are qualitative data.
b. Rankings are numeric but not measurements or
counts, so these are qualitative data.
c. The amounts of dye needed are measured and
therefore are quantitative data.
d. The numbers of paint choices must be counted, so
they are quantitative data as well.
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1.2 Data Classifications
Continuous vs. Discrete:
Qualitative
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Quantitative
DISCRETE
Continuous
Usually
counts of
things
Usually
measurements
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Example 1.5: Classifying Data as Continuous or
Discrete
Determine whether the following data are continuous
or discrete.
a. Temperatures in Fahrenheit of cities in South
Carolina
b. Numbers of houses in various neighborhoods in a
city
c. Numbers of elliptical machines in every YMCA in
d. Heights of doors
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Example 1.5: Classifying Data as Continuous or
Discrete (cont.)
Solution
a. Temperatures could be measured to any level of
precision based on the thermometer used, so these
are continuous data.
b. Numbers of houses are discrete data because
houses are counted in whole numbers. A house
under construction is still a house.
c. The numbers of elliptical machines are counts, so
these are discrete data.
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Example 1.5: Classifying Data as Continuous or
Discrete (cont.)
d. Heights are measurements and again, depending on
the ruler, the heights could be measured to any level
of precision, so they are continuous data.
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1.2 Data Classifications
Levels of Measurement
Ratio
Interval
Ordinal
0 means the
absence of
something
0 is a
placeholder
Order
Nominal
Names
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1.2 Data Classifications
Levels of Measurement
NOMINAL – Names, Categories
Calculations are not applicable.
Example: Favorite Pizza Topping
Nominal
Names
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Example 1.6: Understanding the Nominal Level
of Measurement
a. Suppose all students in a statistics class were asked
what pizza topping is their favorite. Explain why
these data are at the nominal level of measurement.
b. Suppose instead that you wish to know the number
of students whose favorite pizza topping is sausage.
Explain why this data value is not at the nominal
level of measurement.
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Example 1.6: Understanding the Nominal Level
of Measurement (cont.)
Solution
a. These data are nominal because the data simply
describe or label the different toppings of the pizza.
b. In the second scenario, the data value is a count of
students who prefer sausage. This data value is
quantitative, not qualitative, so it is not a label and
would not be considered to be at the nominal level
of measurement.
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1.2 Data Classifications
Levels of Measurement
ORDINAL – Can be arranged in a meaningful order
But arithmetic calculations are not applicable.
EXAMPLE – The seat number on
Ordinal
Order
Nominal
Names
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Example 1.7: Classifying Data as Nominal or
Ordinal
Determine whether the data are nominal or ordinal.
a. The seat numbers on your concert tickets, such as
A23 and A24
b. The genres of the music performed at the 2013
Grammys
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Example 1.7: Classifying Data as Nominal or
Ordinal (copy)
Solution
a. Seat numbers are ordinal because there is a
meaningful order to the data, namely, the position
in the theater.
b. Despite the fact that you may have your own
personal preference for specific genres of music,
there is no standard order. Therefore, music genres
are nominal data.
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1.2 Data Classifications
Levels of Measurement
INTERVAL – 0 might be present but it doesn’t mean the absence
of something. Addition & Subtraction okay.
Multiplication & Division not applicable
EXAMPLES: Fahrenheit temps,
Certain exam scores (like IQ test),
Interval
Calendar dates
0 is a
placeholder
Ordinal
Order
Nominal
Names
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1.2 Data Classifications
Levels of Measurement
RATIO – Zero really means the absence of something
Multiplication and Division make sense.
EXAMPLES: Kelvin temperature,
Interval
Price of a product,
0 is a
Time to run a race
placeholder
Ratio
0 means the
absence of
something
Ordinal
Order
Nominal
Names
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Example 1.8: Classifying Data by the Level of
Measurement
The birth years of your classmates are collected. What
level of measurement are these data?
Solution
Birth years can be ordered. It is also meaningful to
subtract years to determine the difference in age.
However, the year 0 A.D. does not mean the beginning
of time. Therefore, birth years are at the interval level
of measurement.
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Levels of Measurement
Qualitative data consist of labels or descriptions of
traits.
Quantitative data consist of counts or measurements.
Continuous data are quantitative data that can take on
any value in a given interval and are usually
measurements.
Discrete data are quantitative data that can take on
only particular values and are usually counts.
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Levels of Measurement
Data at the nominal level of measurement are
qualitative data consisting of labels or names.
Data at the ordinal level of measurement are
qualitative data that can be arranged in a meaningful
order, but calculations such as addition or division do
not make sense.
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Levels of Measurement
Data at the interval level of measurement are
quantitative data that can be arranged in a meaningful
order, and differences between data entries are
meaningful.
Data at the ratio level of measurement are quantitative
data that can be ordered, differences between data
entries are meaningful, and the zero point indicates the
absence of something.
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Example 1.9: Classifying Data by the Level of
Measurement
Consider the ages in whole years of US presidents
when they were inaugurated. What level of
measurement are these data?
Solution
The ages of US presidents are measurable, can be
ordered, and an age of zero indicates the absence of
life. Therefore, ages are at the ratio level of
measurement. In contrast to Example 1.8, involving
birth years, you can be twice as old as someone else.
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Classify the Credit Score measurement
• Qualitative or Quantitative?
• If quantitative, is it ordinal or interval or ratio?
(illustration from some web site, maybe my bank?)
Example 1.10: Classifying Data
Determine the following classifications for the given
data sets: qualitative or quantitative; discrete,
continuous, or neither; and level of measurement.
a. Finishing times for runners in the Labor Day 10K
race
b. Colors contained in a box of crayons
c. Boiling points (on the Celsius scale) for various
caramel candies
d. The top ten Spring Break destinations as ranked by
MTV
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Example 1.10: Classifying Data (cont.)
Solution
a. The amount of time it takes for each runner to run
the race is quantitative since calculations performed
on these data are meaningful. A finishing time is a
measurement, therefore the data are continuous.
Differences between finishing times are meaningful,
and a time of zero represents the absence of racing.
We could also say that Andrew finished the race in
half of Peyton’s time; thus, the data are at the ratio
level of measurement.
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Example 1.10: Classifying Data (cont.)
b. Colors are labels, so these data are qualitative.
Qualitative data are neither discrete nor continuous.
There are many ways to order colors, such as
alphabetically or based on the color spectrum.
However, when discussing colors of crayons, order is
not the primary factor, as opposed to data such as
rankings, in which order is important. Therefore, the
data are at the nominal level of measurement.
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Example 1.10: Classifying Data (cont.)
c. Calculations can be performed on boiling points
because they are measurements, making these data
quantitative. Temperatures are measurements, so
the data are continuous. For the Celsius scale, a
temperature of zero degrees is simply a placeholder
and does not indicate the absence of heat.
Therefore, data from the Celsius scale are always at
the interval level of measurement.
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Example 1.10: Classifying Data (cont.)
d. Since the rankings cannot be meaningfully added or
subtracted, the data must be qualitative. Qualitative
data are neither discrete nor continuous. The
rankings are in a specific order, so the data are at
the ordinal level of measurement.
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