Math 160 - Cooley
Intro to Statistics
OCC
Section 1.1 – Statistics Basics
Descriptive Statistics – Descriptive statistics consists of methods for organizing and summarizing information.
This includes the construction of graphs, charts, and tables and the calculation of various descriptive measures
such as averages, measures of variation, and percentiles.
Population – The collection of all individuals or items under consideration in a statistical study.
Sample – That part of the population from which information is obtained.
Inferential Statistics – Inferential statistics consists of methods for drawing and measuring the reliability of
conclusions about a population based on information obtained from a sample of the population.
Observational study – A study where researches simply observe characteristics and take measurements, as in a
sample survey.
Designed experiment – A study where researchers impose treatments and controls and then observe
characteristics and take measurements.
 Exercises:
For questions 1 through 3, classify each of the studies as either descriptive or inferential. Explain your answer.
1)
Professional Athlete Salaries. From the Statistical Abstract of the United States, and the article
“Average Salaries in the NBA, NFL, and MLB”, published on the Yahoo! Contributor Network, we
obtained the following data on average professional athletes’ salaries for the years 2005 and 2011.
Sport
Baseball (MLB)
Basketball (NBA)
Football (NFL)
2)
Average Salary ($millions)
2005
2011
2.48
3.31
4.04
5.15
1.40
1.90
Drug Use. The US. Substance Abuse and Mental Health Services Administration collects and publishes
data on drug use, by type of drug and age group, in National Household Survey on Drug Abuse. The
following table provides data for the years 2003 and 2008. The percentages shown are estimates for the
entire nation based on information obtained from a sample.
Type of drug
Any illicit drug
Marijuana and hashish
Cocaine
Hallucinogens
Inhalants
Any psychotherapeutic
Alcohol
“Binge” alcohol use
Cigarettes
Smokeless tobacco
Cigars
Percentage, 18-25 years old
Ever used
Current user
2003
2008
2003
2008
60.5
56.6
20.3
19.6
53.9
50.4
17.0
16.5
15.0
14.4
2.2
1.5
23.3
17.7
1.7
1.7
14.9
10.4
0.4
0.3
29.0
29.2
6.0
5.9
87.1
85.6
61.4
61.2
N/A
N/A
41.6
41.8
70.2
64.2
40.2
35.7
22.0
20.3
4.7
5.4
45.2
41.4
11.4
11.3
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Math 160 - Cooley
Intro to Statistics
OCC
Section 1.1 – Statistics Basics
 Exercises:
3)
The Music People Buy. Results of monthly telephone surveys yielded in the percentage estimates of all
music expenditures shown in the following table. These statistics were published in 2007 Consumer
Profile. [SOURCE: Recording Industry Association of America, Inc.]
Music Type
Rock
R&B/Urban
Country
Rap/Hip-Hop
Pop
Other
Religious
Children’s
Jazz
Unknown
Classical
Soundtracks
Oldies
New Age
4)
5)
Expenditure (%)
32.4
11.8
11.5
10.8
10.7
7.1
3.9
2.9
2.6
2.5
2.3
0.8
0.4
0.3
Pricey Gasoline. An Associated Press / AOL pool of 1000 U.S. adults, taken April 18-20, 2005 and
appearing in the Eau Claire Leader Telegram on April 22, asked about some of the consequences of the
rising cost of gasoline. Of those sampled, 58% had reduced their driving, 57% had cut back on other
expenses, 41% had planned vacations closer to home, and 41% said that they may buy a more
fuel-efficient vehicle.
a)
Identify the population and sample for this study.
b)
Are the percentages provided descriptive statistics or inferential statistics? Explain your answer.
Do Left-Handers Die Earlier? According to a study published in the Journal of the American Public
Health Association, left-handed people do not die at an earlier age than right-handed people, contrary to
the conclusion of a highly publicized report done 2 years earlier. The investigation involved a 6-year
study of 3800 people in East Boston older than age 65. Researchers at Harvard University and the
National Institute of Aging found that the “lefties” and “righties” died at exactly the same rate. “There
was no difference, period,” said Dr. Jack Guralnik, an epidemiologist at the institute and one of the
coauthors of the report. Is this investigation an observational study or a designed experiment? Justify
your answer.
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Math 160 - Cooley
Intro to Statistics
OCC
Section 1.1 – Statistics Basics
 Exercises:
6)
Aspirin and Cardiovascular Disease. In an article by P. Ridker et al. titled “A Randomized Trial of
Low-dose Aspirin in the Primary Prevention of Cardiovascular Disease in Women” (New England
Journal of Medicine, Vol. 352, pp. 1293-1304), the researchers noted that “We randomly assigned
39,876 initially healthy women 45 years of age or older to receive 100 mg of aspirin or placebo on
alternate days and then monitored them for 10 years for a first major cardiovascular event (i.e., nonfat
myocardial infraction, nonfatal stroke, or death from cardiovascular causes).” Is this investigation a
designed experiment or an observational study? Explain your answer.
7)
Starting Salaries. The National Association of Colleges and Employees (NACE) compiles information
on salary offers to new college graduates and publishes the results in Salary Survey. Are these statistical
studies designed experiments or observational studies? Explain your answer.
 Answers to Exercises:
1)
Descriptive; It is a summary of the average salaries in professional baseball, basketball, and football for
2005 and 2011.
2)
Inferential; National samples are used to make estimates (or inferences about) drug use through the
entire nation.
3)
Inferential; Monthly survey data is used to make estimates of the percentages of all music expenditures.
4a)
The population consists of all U.S. adults. The sample consists of the 1000 U.S. adults who were
surveyed.
4b)
The percentages provided are descriptive statistics since they described the consequences of higher
gasoline prices for the 1000 people surveyed. There does not seem to be an attempt to claim that these
percentages apply to the entire population of the U.S.
5)
Observational Study; The researchers at Harvard University and the National Institute of Aging simply
observed the two groups.
6)
Designed Experiment; The researchers did not simply observe the two groups of women, but instead
randomly assigned one group to receive aspirin and the other to get a placebo.
7)
Observation Studies; The researchers simply collected available information about the starting salaries
of new college graduates.
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