Statistics
Introduction to Statistics
Chapter 1 – 2
Data Classification
Types of Data:
1) Qualitative Data – consists of attributes, labels, or nonnumerical entries
2) Quantitative Data – consists of numerical measurements or counts
Example 1
The base prices of several vehicles are shown in the table. Which data are qualitative data and
which are quantitative data? Explain your reasoning.
Model
Base Price
Focus SE
$17,795
F-150 XL
$18,710
Fusion SE
$23,785
Escape XLT Sport
$25,575
Explorer
$26,775
Flex
$28,500
Taurus
$28,830
Expedition XLT
$35,480
Levels of Measurement:
1) Nominal Level of Measurement – Only qualitative. Data at this level are
categorized using names, labels, or qualitites. No mathematical computations can
be made at this level
2)Ordinal Level of Measurement – qualitative or quantitative. Data at this
level can be arranged in order, or ranked, but differences between data entries are
not meaningful
Example 2
Two data sets are shown. Which data set consists of data at the nominal level? Which data set
consists of data at the ordinal level? Explain your reasoning.
Top Five TV Programs
(from 2/12/12 to 2/18/12)
1. American Idol – Tuesday
Network Affiliates in
Pittsburgh, PA
2. American Idol –
WTAE (ABC)
Wednesday
3. Grey’s Anatomy
WPXI
(NBC)
4. House
KDKA
(CBS)
5. CSI
WPGH
(FOX)
The two highest levels of measurement
3) Interval Level of Measurement – can be ordered, and you can calculate
meaningful differences between data entries. At the interval level, a zero entry
simply represents a position on a scale, the entry is not an inherent zero
4) Ratio level of Measurement – 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.
Inherent zero – A zero that implies “none”
Example 3
Two data sets are shown. Which data set consists of data at the interval level? Which data set
consists of data at the ratio level? Explain your reasoning.
2010 American League
Home Run Totals (by
Team)
Baltimore
164
New York Yankees’
Boston
192
World Series Victories (Years)
Chicago
236
1923, 1927, 1928, 1932, 1936
Cleveland
196
1937, 1938, 1939, 1941, 1943
Detroit
203
1947, 1949, 1950, 1951, 1952
Kansas City
124
1953, 1956, 1958, 1961, 1962
Los Angeles
159
1977, 1978, 1996, 1998, 1999,
Minnesota
143
2000
New York
210
Oakland
175
Seattle
172
Tampa Bay
190
Texas
183
Toronto
199
Use the following tables to summarize which operations are meaningful at each of the four levels
or measurement.
Level of
Put data in Arrange data
Subtract
Determine if one data
Measurement
categories
in order
data values
value is a multiple of
another
Example of a Data Set
Nominal Level
(Qualitative data)
Ordinal Level
(Qualitative or
Quantitative data)
Interval Level
(Quantitative data)
Ratio Level
(Quantitative data)
Meaningful Calculations