Sect. 1-2 Data Classification
Objective: SWBAT distinguish between
Qualitative and Quantitative data
Also be able to classify data in the four
levels of measurement Nominal,
Ordinal, interval, and ratio.
In this section you will learn to classify data by
type and by level of measurement. Data sets can
consist of two types of data: Qualitative data
and quantitative data
Definition
Qualitative Data Consists of attributes, labels , or non
numerical entries.
Quantitative Data : Consists of numerical measurements
or counts.
Example
The names are Non
numerical entries so
these are qualitative
data.
The base price of several vehicles are
shown in the table, Which data sets
are qualitative and which are
quantitative.
Model
Base Price
Ranger XL
ZX2
Focus LX
Taurus LX
Explorer
Sport-Trac
Windstar
LX 3-Door
Crown
Victoria
Expedition XLT
$12,595
$12,750
$13,120
$19,075
$22,510
$22,740
$22,835
$30,855
The base prices are
numerical entries so these
are quantitative data.
Levels of measurement
Another data characteristic is the data’s level of
measurement. The level of measurement determine
which statistical calculations are meaningful. The four
levels of measurement in order from lowest to highest,
are nominal , ordinal, interval, and ratio.
Definition
data at the nominal level of measurement are qualitative only. Data at this
level are categorized using names, labels, or qualities. No mathematical
computation can be made at this point.
Data at the ordinal level of measurement are qualitative or quantitative
Data at this level can be arranged in order, but differences between data are
not meaningful.
Example
Classifying Data by Level
Two data sets are shown. Which data set consist of data at the
nominal level and which data set consist of data at the ordinal level.
Top 5 T V Programs
(from 5-14-01 to 5-20-01
1. ER
2. Friends
3. Law and Order
4. West Wing
5. Will and Grace
Network Affiliates in
Portland , Oregon
KATV
KGW
KOIN
KPDX
(ABC)
(NBC)
(CBS)
(FOX)
The first data set lists the rank of the TV programs. The data consists of the ranks
1,2,3,4, and 5. Because the rankings can be listed in order, these data are at the
ordinal level. Note that the difference between rank of 1 and 5 has no mathematical
meaning. The second data set consists of the call letters of each network affiliate in
Portland. The call letters are simply the names of network affiliates so these data are
at the nominal level.
Try it Yourself
Consider the following data sets. For each data
set decide whether the data are at the nominal
level or the ordinal level.
1. The final standings of the Northern Division
of the National Hockey League.
2. A collection of phone numbers.
a. Identify what each data set represents.
b. Specify the level of measurement
Definition
Data at the interval level of measurement are
quantitative the data 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.
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 tow
data values can be formed so one data value can be
expressed as a multiple of another.
Example
Two data sets are shown below . Which set consists
of the data at the interval level? Which set consists
of data at the ratio level? Explain your reasoning.
American league
Home run totals (by Teams)
Anaheim
Baltimore
Boston
Chicago
Cleveland
Detroit
Kansas City
Minnesota
New York
Oakland
Seattle
Tampa Bay
Texas
Toronto
236
184
167
216
221
177
150
116
205
239
198
162
173
244
New York Yankees
World Series Victories (years)
1923,1927, 1928,1932, 1936, 1937,
1938, 1939, 1941, 1943, 1947, 1949,
1950,1951,1952, 1953,1956, 1958,
1961, 1962 , 1977, 1978, 1996,
1998, 1999, 2000
Examples of a Data Set
Meaningful Calculations
Summary
four
of Measurement
Nominal
Level of
Major
PGAlevels
Tournament
Put in a category
(Qualitative Set) The masters
For example These are four
The U.S. Open
categories of major PGA
The British Open
To urnaments
The PGA Championship
Ordinal Level
(Qualitative or
Quantitative
Set)
Motion Picture Association of Put in a category and in order
America ratings Description
For instance a PG rating has a
G General Admission
stronger restriction than a G
PG Parental Guidance
rating.
PG-13 Parents Strongly
Cautioned
R Restricted
NC-17 17 and Under Not
permitted
Interval Level
Quantitative
Data
Average Temp for
Sacramento, Calif.
Jan. 45.3 Feb. 50.3, Mar.
53.2, Apr. 58.2, …
Put in a category ,put in order ,
and find difference in values
For instance 50.3-45.3 =5
So Feb. was 50 warmer than
January
Ratio level
Quantitative
Average Monthly
precipitation (in inches) for
Put in a category ,put in order ,
and find difference in values and
Homework 1-20 pgs.12-13
Section 1.2
Data Classification
Levels of Measurement
A data set can be classified according to the
highest level of measurement that applies. The four
levels of measurement, listed from lowest
to highest are:
1. Nominal
2. Ordinal
3. Interval
4. Ratio
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Levels of Measurement
1. Nominal:Categories, names, labels, or qualities.
Cannot perform mathematical operations on this
data.
Ex: type of car you drive, your major
2. Ordinal:Data can be arranged in
order. You can say one data entry is
greater than another.
Ex: TV ratings, condition of patient in hospital
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Levels of Measurement
3. Interval: Data can be ordered and
differences between 2 entries can be
calculated. There is no inherent zero (a zero
that means “none”).
Ex: Temperature, year of birth
4. Ratio: There is an inherent zero. Data
can be ordered, differences can be found,
and a ratio can be formed so you can say
one data value is a multiple of another.
Ex: Height, weight, age
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