Section 1.1 - An Overview of Statistics
Summer 2013 - Math 1040
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Roadmap
We want to understand:
Fundamental terminology of data and statistics.
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Data and statistics
We collect data, or information that comes from observations, responses,
measurements, or counts. Statistics is the science of information that
collects, organizes, analyzes, and interprets data. We use statistics to
describe data, make predictions, and make decisions.
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Populations and Samples
Data sets come in two types:
A population is the collection of all possible outcomes, responses,
measurements, or counts.
A sample is any subset, or part, of a population.
Example: 19% of Indiana 9th graders in one school district said they
smoked cigarettes daily.
Path to the Solution: Decide (i) what group you are interested in
and (ii) what part of it may best represent that group.
Possible solution: All Indiana 9th grade students is the population.
The sample is the students of one school district.
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Identify the Population and Sample
Identify the population and sample:
1
A survey of 1400 American households found that 18% of the
households own one or more computers.
2
A recent survey of 2600 elementary school children found that 28% of
the children could be classified as obese.
3
The mean weight of every sixth person entering a shopping mall
within a 2 hour period was 146 lb.
4
The average annual salary for 35 of a company’s 1200 accountants is
$68,000.
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Parameters and Statistics
A parameter is a numerical1 description of a population
characteristic.
A statistic is a numerical description of a sample characteristic.
Parameters are often unknown. Imagine if you have the exact mean time
for any adult to run a mile. Would it be easy or difficult to obtain this
value? Instead what would you use for an estimate?
Statistics estimate parameters, and we will be studying if the estimates we
are able to obtain are suitable.
1
It may be non-numeric
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Identify the Parameter and Statistic
Identify which relevant numerical value is a parameter or a statistic.
(Explain.)
1
A recent survey by the alumni of a major university indicated that the
average salary of 10,000 of its 300,000 graduates is $125,000.
2
The mean weight of every sixth person entering a shopping mall
within a 2 hour period was 146 lb.
3
The average annual salary for 35 of a company’s 1200 accountants is
$68,000.
4
19% of a sample of Indiana 9th graders said they smoked cigarettes
daily.
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Putting it all together.
What are the populations and samples? What are the parameters and
statistics?
1
A survey of 1000 U.S. adults found that 92% are worried about
dependance on foreign oil.
2
38 nurses working in the San Francisco area were surveyed concerning
their opinions of managed health care.
3
A study of 146 credit cards found that the average late fee is $27.46.
4
Astronomers determine the distance to a galaxy by measuring the
distance to just a few stars within it and taking the mean of these
distance measurements.
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Descriptive and Inferential Statistics
1
The organization, summerization, and display of data is involved in
the branch of study known as descriptive statistics.
2
Inferential statistics is the branch of statistics that involves using a
sample to draw conclusions about a population.
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Stanley Smith Stevens
Stanley Smith Stevens
1906 - 1973
Introduced, ”levels of
measurement,” in his 1946
paper, ”On The Theories of
Scales of Measurement.”
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Assignments
Assignment:
1
Read pages 2 through 5.
2
Draw conclusions from the examples in these slides using inferential
statistics.
Vocabulary:
Data, population, sample, parameter, statistic (the sample characteristic),
descriptive statistics, inferential statistics.
Understand:
Identify the differences between populations and samples, parameters and
statistics, and identify descriptive statistics and inferential statistics.
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