Section 1.2 - Data Classification
Summer 2013 - Math 1040
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Roadmap
Today we look into:
Classification of scales of measurement.
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Data Classification
Data falls into two types:
Data that consists of attributes, labels or nonnumerical entries is
qualitative.
Data that consists of numerical measurements or counts is called
quantitative.
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Examples
Identify the data set. Decide if the data is qualitative or quantitative.
The heights of hot air balloons.
Eye colors of celebrities.
Carrying capacity of pickups.
Student ID numbers.
ZIP codes.
Species of trees in a forest.
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Four levels of measurement
Here is a table listing some examples of levels of measurement:
L. O. M.
nominal
Data Type
qualitative only
ordinal
interval
either qualitative
or quantitative
quantitative only
ratio
quantiative only
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Example
Injury Location
Social Security Number
Mineral Hardness
Personality Trait
Temperature
Years Italy wins a World Cup
Population counts
length, width
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Nominal and ordinal levels of measurement
Nominal data are qualitative data like names, labels, or qualities.
There are no meaningful ordering or mathematical computations.
Ordinal data are either qualitative or quantitative. Data can be
ranked, but means, standard deviations, and differences are not
meaniful.
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Example - Case Study on TV Ratings
Identify the data sets, and decide if they are nominal or ordinal.
Rank
1
2
3
4
5
6
7
8
8
10
Rank Last Week
1
2
3
4
5
7
8
10
8
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Program Name
American Idol - Tuesday
American Idol - Wednesday
Grey’s Anatomy
House
CSI
CSI: Miami
Desparate Housewives
Deal or No Deal - Monday
Two and a Half Men
Shark
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Network
FOX
FOX
ABC
FOX
CBS
CBS
ABC
NBC
CBS
CBS
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Interval and ratio levels of measurement
Interval data is quantitative data that can be ordered and arithmetic
like sums, differences and means are meaningful. Zero points are a
matter of convenience or convention - they are not inherent in the
measurement.
Ratio data is quantitative data in which zero points are inherent
zeroes, and multiples and ratios have a meaningful interpretation.
Inherent zeroes are zeroes that imply the concept of “none.” Credit card
balances of $0 means there is no debt to repay, but something like
0-one-hundred-hours, or midnight, does not mean the absence of time.
Centigrade and Fahrenheit scales of temperature are useful examples of
interval data types.
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Exampels - Slide 1 of 2
Which data set consists of data at the interval level? Which data set
consists of data at the ratio level?
Salt Lake City Bees’ Division Titles (years)
1995, 1999, 2000, 2002
2006, 2007, 2008
Pacific Conference 2012 Home Run Totals (by team)
Colorado Springs
Reno
Salt Lake
Tacoma
Fresno
Las Vegas
Sacramento
Tuscon
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103
116
143
152
122
133
171
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Examples - Slide 2 of 2
Identify the data sets, and decide if they are interval or ratio.
Help: Does 0 mean ”nothing / none?”
1
The year of release of the top 10 drama movies.
2
The amount of sugar (in grams) in two dozen cookies.
3
The body temperature (in degrees Fahrenheit) of an athlete during an
exercise session.
4
The heart rates (in beats per minute) of an athlete during an exercise
session.
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Assignements
Assignment:
1
Read pages 9 through 12.
2
The recommended exercises.
3
Extra: Identify the level of measurement for each of the four types
from articles on the web, in a magazine, or in a newspaper.
Vocabulary:
Qualitative data, quantitative data, nominal level, ordinal level, interval
level, ratio level.
Understand:
Identify the type of data set (qualitative or quantitative) and one of the
four levels of measurement for the data.
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