### Homework Answers 1.1 1. A sample is a subset of a population. 2.

```Homework Answers 1.1
1. A sample is a subset of a population.
2. It is usually to impractical (too expensive and timeconsuming) to obtain all the population data.
3. False
4. True
5. True
6. False
7. Population
8. Sample
9. Sample
10. Population
11. Population: Party of registered voters in Bucks County.
Sample: Party of Bucks County voters responding to a
phone survey.
12. Population: Major of college students at Central
College.
Sample: Major of college students at Central College who
13. Population: Ages of adult Americans who own
computers.
Sample: Ages of adult Americans who own Dell computers.
14. Population: Income of all home owners in Ohio.
Sample: Income of home owners in Ohio with mortgages.
15. population: Collection of all infants.
Sample: Collection of the 33,043 infants in the study.
16. Population: Collection of all American households
Sample: Collection of the 1023 American households
surveyed.
17. Population: Collection of all American women.
Sample: Collections of the 546 American women surveyed.
18. Population: Collection of all American vacationers
Sample: Collection of the 872 American vacationers
surveyed.
19. statistic
20. statistic
21. statistic
22. parameter
23. The statement “56% are the primary investor in their
household” is an application of descriptive statistics.
An inference drawn from the sample is that an association
exists between American women and the primary
investor in their household.
24. The statement “spending at least \$1800 for their next
vacation” is an application of descriptive statistics.
An inference drawn from the sample is that American
vacationers are associated with spending more than
\$1800 for their next vacation.
1.2 Data Classification
Statistics
Mrs. Spitz
Fall 2008
Objectives
• How to distinguish between qualitative data and
quantitative data.
• How to classify data with respect to the four levels of
measurement: nominal, ordinal, interval, and ratio
Assignment
• Pgs. 12-13 #1-20 all
Definitions
• Qualitative data consist of attributes, labels or nonnumerical entries.
• Quantitative data consist of numerical measurements
or counts.
Ex. 1 Classifying Data by Type
• The base price of several
vehicles are shown in the
table. Which data are
qualitative and which are
quantitative data? Explain
Model
Escort LX
Ranger 4x2 XL
Contour LX
Base Price
\$11,430
\$11,485
\$14,460
Taurus LX
Windstar
\$18,445
\$19,380
\$21,560
Explorer XL 4x2
Crown Victoria
Expedition 4x2
XLT
\$21,135
\$28,255
Ex. 1 Classifying Data by Type
• Solution: The information
shown in the table can be
separated into other data
sets. One data set contains
the names of the vehicle
models and the other
contains base prices of
vehicle models. The names
are non-numerical entries
are qualitative data. The
base prices are numerical,
Model
Escort LX
Ranger 4x2 XL
Contour LX
Base Price
\$11,430
\$11,485
\$14,460
Taurus LX
Windstar
\$18,445
\$19,380
\$21,560
Explorer XL 4x2
Crown Victoria
Expedition 4x2
XLT
\$21,135
\$28,255
Ex. 2 – Try it yourself
City
Population City
Population
Baltimore, 702,979
MD
Las Vegas, 327,878
NV
Boston, MA 547,725
Lincoln, NE 203,076
Dallas, TX
Seattle,
WA
1,022,830
520,947
• The populations of several
US cities are shown in the
table. Which data are
qualitative and which are
quantitative?
A. ID the contents of the data
set.
B. Decide whether the data
consist of numerical or nonnumerical entries.
Ex. 2 – Try it yourself
A. City population
B. City – non-numerical
Population: Numerical
C. City: Qualitative
Population: Quantitative
• The populations of several
US cities are shown in the
table. Which data are
qualitative and which are
quantitative?
A. ID the contents of the data
set.
B. Decide whether the data
consist of numerical or nonnumerical entries.
Levels of Measurement
• Another data characteristic is the data’s level of
measurement. The level of measurement determines
which statistical calculations are meaningful. The four
levels of measurement, in order from lowest to highest
are nominal, ordinal, interval and ratio.
• When numbers are at the nominal level of measurement,
the simply represent a label. Examples of numbers used
as labels include social security numbers, and numbers
on sports jerseys.
Definitions
• Nominal Level – Data in 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 – Data at the nominal level of
measurement are qualitative or quantitative. Data at
this level can be arranged in order, but differences
between data entries are not meaningful.
Ex. 3 Classifying data by level
Top 5 TV Programs
• Two sets of data are shown.
Which data set consists of
data at the nominal level?
Which data set consists of
data at the ordinal level?
Seinfeld
ER
Veronica’s Closet
Friends
NFL Monday Night Football
Network affiliations (Portland, Oregon)
KATU (ABC)
KGW (NBC)
KOIN (CBS)
KPDX (FOX)
Ex. 3 Classifying data by level
• The first data set lists the
rank of five 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
the difference between a
rank of 1 and 5 has no
mathematical meaning.
Top 5 TV Programs
1. Seinfeld
2. ER
3. Veronica’s Closet
4. Friends
5. NFL Monday Night Football
Ex. 3 Classifying data by level
• The second set of data
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.
Network affiliations (Portland, Oregon)
KATU (ABC)
KGW (NBC)
KOIN (CBS)
KPDX (FOX)
Definitions
• Interval Level – Data at the interval level are
quantitative. The data can be ordered and you can
calculate meaningful differences between data entries.
At the interval level, a zero entry is simply representing
a position on a scale; the entry in not an inherent zero.
Definitions
• Ratio Level – Data at the ratio level 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 one data value can be expressed as a
multiple of another.
Note:
• An inherent zero is a zero that implies “none.” For
instance, the amount of money you have in a savings
account could be zero dollars. In this case, the zero
represents no money—it is an inherent zero. On the
other hand, a temperature of 0° does NOT REPRESENT a
condition where no heat is present. The 0°C
temperature is simply a position on the Celsius scale. It
is NOT and inherent zero.
Ex. 4: Classifying data by level
• Two data sets are shown.
Which data set consists of
data at the interval level?
Which data set consists or
data at the ratio level?
New York Yankees’ World Series Victories (Years)
1923 1727 1928 1932 1936
1937 1938 1939 1941 1943
1947 1949 1950 1951 1952
1953 1956 1958 1961 1962
1977 1978 1996 1998
Ex. 4: Classifying data by level
• Both contain quantitative data. Consider
the dates of the Yankees’ World Series
victories. It makes sense to find the
difference between specific dates. For
instance, the time between the Yankees’
first and last World Series victories is
1998 – 1923 = 75 years –
• But it does NOT make sense to write a
ratio using these dates. So, these data
are at the interval level.
New York Yankees’ World Series Victories (Years)
1923 1727 1928 1932 1936
1937 1938 1939 1941 1943
1947 1949 1950 1951 1952
1953 1956 1958 1961 1962
1977 1978 1996 1998
Other Data Set
Using the home run totals, you
can find differences and
write ratios. From the data,
you can see that New York
hit three more homeruns
than Kansas City hit and that
Seattle hit twice as many
homeruns Minnesota hit. So
these data are compared at
the ratio level.
1997 American League Home Run Totals (by team)
Anaheim
161
Baltimore
196
Boston
185
Chicago
158
Cleveland
220
Detroit
176
Kansas City
158
Milwaukee
135
Minnesota
132
New York
161
Oakland
197
Seattle
264
Texas
187
Toronto
147
The following tables summarize meaningful operations at the four
levels of measurement.
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
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