Transcript 1.2 Data Classification

1.2 Data Classification
•How to distinguish between qualitative and
quantitative data
•How to classify data with respect to the four levels
of measurement: nominal, ordinal, interval, and
ratio
Qualitative data
Qualitative data consist of attributes, labels, or nonnumerical
entries.
Quantitative data
Quantitative data consist of numerical measurements or counts.
Try it yourself 1
Classifying Data by Type
The population of several U.S. cities are shown in the table.
Which data are qualitative data and which are quantitative
data? (Source: U.S. Census Bureau)
City
Population
Baltimore, MD
636,919
Jacksonville, FL
807,815
Memphis, TN
669,651
Pasadena, CA
143,080
San Antonio, TX
Seattle, WA
1,351,305
598,541
The two different data sets consist of the
names of the cities and the populations of
the cities. The cities consist of
nonnumerical data and are therefore
qualitative data. The populations are
numerical data and are therefore
quantitative data.
Nominal level of measurement
Data at the nominal level of measurement are qualitative only.
Data at this level are categorized using names, labels, or qualities.
No mathematical computations can be made at this level.
Ordinal level of measurement
Data at the ordinal level of measurement are qualitative or
quantitative. Data at this level can be arranged in order, or ranked,
but differences between data entries are not meaningful.
Try it Yourself 2
Classifying Data by Level
Consider the following data sets. For each data set, decide
whether the data are at the nominal level or at the ordinal
level.
1. The final standings for the Pacific Division of the National
Basketball Association
The final standings represent a ranking of basketball teams.
Ordinal, because the data can be put in order.
2. A collection of phone numbers
The collection of phone numbers represents labels. Nominal,
because no mathematical computations can be made.
Interval level of measurement
Data at the interval level of measurement can be ordered, and
meaningful differences between data entries can be calculated. At
the interval level, a zero entry simply represents a position on a
scale; the entry is not an inherent zero.
Ratio level of measurement
Data at the ratio level of measurement are similar to data at the
interval level, with the added property that a zero entry is an
inherent zero. A ratio of two data values can be formed so that one
data value can be meaningfully expressed as a multiple of another.
Try it yourself 3
Classifying Data by Level
Decide whether the data are at the interval level or at the ratio
level.
1. The body temperatures (in degrees Fahrenheit) of an
athlete during an exercise session
Interval, because the data can be ordered and meaningful differences can be
calculated, but it does not make sense to write a ratio using the
temperatures.
2.
The heart rates (in beats per minute) of an athlete during
an exercise session
Ratio, because the data can be ordered, meaningful differences can be calculated,
the data can be written as a ratio, and the data set contains an inherent zero.
Levels of measurement
The following tables summarize which operations are
meaningful at each of the four levels of measurement. When
identifying a data set’s level of measurement, use the highest
level that applies.
Level of
Measurement
Put data in
categories
Arrange data
in order
Subtract
data values
Determine if one data
value is a multiple of
another
Nominal
Yes
No
No
No
Ordinal
Yes
Yes
No
No
Interval
Yes
Yes
Yes
No
Ratio
Yes
Yes
Yes
Yes