Goals
Notes
Goals:
I
Qualitative Data and Quantitative Data
I
Four Levels of Measurement: nominal, ordinal, interval, and ratio.
TV programs viewed by all households in the U.S.
TV Programs viewed by Nielsen sample
(University of Utah)
Math 1040
1/6
Data Types
Notes
Population and sample data can be organized in two types, and
classifying level of measurements can determine which statistical
procedures can be used.
Data that consists of attributes, labels, or nonnumerical entries are
qualitative.
Examples: Eye color, species of trees in a forest, car models.
Data that consists of numerical measurements or counts are
quantitative.
Examples: Heights of hot air balloons, carrying weight of pickup
trucks, area codes, unit prices of groceries.
(University of Utah)
Math 1040
2/6
Levels of Measurement
Notes
Nonnumerical data cannot have mathematical computations. For
example, it does not make sense to add together two car models.
Qualitative data like names, labels, or qualties are called
nominal level of measurement data.
Data that can be arranged in order like the top law schools in the
U.S., but it still does not have any meaning to do mathematical
computations beyond that. Numerical data like area codes or PINs
also can be arranged in order, but it does not make sense to do
operations like addition or multiplication. Qualitative or quantitative
data than can be ranked, but do not have any meaning like addition,
are called ordinal level of measurement data.
(University of Utah)
Math 1040
3/6
Levels of Measurement
Notes
For quantitative data only there are two more levels of measurement.
Interval level of measurement data is quantitative data that can be
ordered and meaningful differences between entries can be calculated.
A zero entry represents a position on a scale only - they are not an
inherent measurement.
Inherent zeroes imply the concept of ”none.” For example, a checking
account with $0 means the account has no money. In contrast, 0o T is
just a temperature on a scale and does not mean no heat (or energy).
Ratio level of measurement data is quantitative data with inherent
zeroes. It now becomes meaningful to express values as multiples of
another.
(University of Utah)
Math 1040
4/6
More Examples
Notes
Examples: Classify each of the data as qualtitative or quantitative.
Classify the data by levels of measurement (nominal, ordinal, interval,
or ratio).
(A) telephone numbers in a directory
(B) body temperatures of patients in a hospital
(C) entertainment software ratings
(D) jersey numbers on a football team
(E) top five college football teams
(F) responses to an opinion poll
(G) years Italy won the World Cup
(H) political parties of the 113th United States Congress
(I) wait times at a bank
(University of Utah)
Math 1040
5/6
Assignment
Notes
For May 19 - 2014
I
§1.2 # 31, 32 (Due: May 21)
I
Read §1.3 by May 21.
For #31, please include examples you may see in your college major.
Suggested Exercises: 1, 2, 21, 22, 29, 30
You should be able to: You should be able to:
I
Distinguish between qualitative data and quantitative data.
I
Classify data as (qualitative): nominal or ordinal.
I
Classify data as (quantitative): interval or ratio.
(University of Utah)
Math 1040
6/6