Chapter 1
Introduction
1.1 Basic Definitions and Concepts
o To learn basic definitions used in statistics and some of its key concepts.
Section Outline
There are millions of passenger automobiles in the United States. What is their
average value?
The best way to solve this problem would be to estimate the average. One
natural way to do so would be to randomly select some of the cars, say 200
of them, ascertain the value of each car, and find the average of the 200
numbers.
The set of all those millions of vehicles is called the population of interest,
and the number attached to each one, its value, is a measurement.
A population is any specific collection of objects of interest.
A measurement is a number or attribute computed for each
member of a population or of a sample.
The average value is a parameter: a number that describes a characteristic of
the population, in this case, monetary worth.
A parameter is a number that summarizes some aspect of the
population as a whole.
The set of 200 cars selected from the population is called a sample, and the
200 numbers—the monetary values of the cars we selected—are the sample
data.
, A sample is any subset or subcollection of the population, including
the case that the sample consists of the whole population, in which
case it is termed a census.
The measurements of sample elements are collectively called the
sample data.
The average of the data is called a statistic: a number calculated from the
sample data.
If the average value of the cars in our sample was $8357, then it seems
reasonable to conclude that the average value of all cars is about $8357.
In reasoning this way we have drawn an inference about the
population based on information obtained from the sample.
Statistics is a collection of methods for collecting, displaying, analyzing, and
drawing conclusions from data.
Descriptive statistics is the branch of statistics that involves organizing,
displaying, and describing data.
Computing the single number $8357 to summarize the data was an
operation of descriptive statistics.
Inferential statistics is the branch of statistics that involves drawing
conclusions about a population based on information contained in a sample
taken from that population.
Using the single number $8357 to make a statement about the
population was an operation of inferential statistics.
The measurement made on each element of a sample need not be numerical.
In the case of automobiles, what is noted about each car could be its color, its
make, or its body type. Such data are categorical or qualitative, as opposed
to numerical or quantitative data such as value or age. This is a general
distinction.
Qualitative data are measurements for which there is no natural
numerical scale, but which consist of attributes, labels, or other
nonnumerical characteristics.
Quantitative data are numerical measurements that arise from a
natural numerical scale.
, The relationship between a population of interest and a sample drawn from
that population is the most important concept in statistics, since everything
else rests on it.
In our same sample of 200 cars, if 172 cars in the sample are less
than six years old, which is 0.86 or 86%, then we would estimate the
parameter of interest—the population proportion—to be about the
same as the sample statistic, the sample proportion: about 0.86.
Key Takeaways
Statistics is a study of data: describing properties of data (descriptive statistics) and
drawing conclusions about a population based on information in a sample
(inferential statistics).
The distinction between a population together with its parameters and a sample
together with its statistics is a fundamental concept in inferential statistics.
Information in a sample is used to make inferences about the population from which
the sample was drawn.
Teaching Tips
Before introducing the basic concepts of statistics, the instructor can discuss the
importance of statistics and how it has helped millions of researchers analyze and
interpret data to arrive at conclusions and understand their topic area of interest in
greater detail.
Instructors can then ask the students to come up with examples of situations where
the use of statistics would be required to arrive at specific conclusions for a particular
topic of study. The instructor can use any of these examples to explain the basic
concepts mentioned in this section.
, Alternative Examples
A group of researchers is conducting a study on the percentage of Chinese products
being consumed by U.S. consumers, in comparison to products from other countries
(including the U.S.) and their products’ quality. They want to find out if the usage of
Chinese products is increasing every year and if they are likely to completely
dominate the U.S. market in the near future.
A group of car enthusiasts wants to know what percentage of ethanol-gas mixture is
sold for consumers’ use in the U.S.
1.2 Overview
o To obtain an overview of the material in the text.
Section Outline
The example discussed in the previous section is fairly simple. However, it
illustrates some significant problems.
The sample average is an example of what is called a random variable: a
number that varies from trial to trial of an experiment.
In the example, we have supposed that the 200 cars of the sample
had an average value of $8357 (a number that is precisely known),
and concluded that the population has an average of about the same
amount, although its precise value is still unknown. However, it is
almost certain that we will get a different sample average if we take
another sample of exactly the same size from exactly the same
population.
Different samples have different levels of reliability.
Introduction
1.1 Basic Definitions and Concepts
o To learn basic definitions used in statistics and some of its key concepts.
Section Outline
There are millions of passenger automobiles in the United States. What is their
average value?
The best way to solve this problem would be to estimate the average. One
natural way to do so would be to randomly select some of the cars, say 200
of them, ascertain the value of each car, and find the average of the 200
numbers.
The set of all those millions of vehicles is called the population of interest,
and the number attached to each one, its value, is a measurement.
A population is any specific collection of objects of interest.
A measurement is a number or attribute computed for each
member of a population or of a sample.
The average value is a parameter: a number that describes a characteristic of
the population, in this case, monetary worth.
A parameter is a number that summarizes some aspect of the
population as a whole.
The set of 200 cars selected from the population is called a sample, and the
200 numbers—the monetary values of the cars we selected—are the sample
data.
, A sample is any subset or subcollection of the population, including
the case that the sample consists of the whole population, in which
case it is termed a census.
The measurements of sample elements are collectively called the
sample data.
The average of the data is called a statistic: a number calculated from the
sample data.
If the average value of the cars in our sample was $8357, then it seems
reasonable to conclude that the average value of all cars is about $8357.
In reasoning this way we have drawn an inference about the
population based on information obtained from the sample.
Statistics is a collection of methods for collecting, displaying, analyzing, and
drawing conclusions from data.
Descriptive statistics is the branch of statistics that involves organizing,
displaying, and describing data.
Computing the single number $8357 to summarize the data was an
operation of descriptive statistics.
Inferential statistics is the branch of statistics that involves drawing
conclusions about a population based on information contained in a sample
taken from that population.
Using the single number $8357 to make a statement about the
population was an operation of inferential statistics.
The measurement made on each element of a sample need not be numerical.
In the case of automobiles, what is noted about each car could be its color, its
make, or its body type. Such data are categorical or qualitative, as opposed
to numerical or quantitative data such as value or age. This is a general
distinction.
Qualitative data are measurements for which there is no natural
numerical scale, but which consist of attributes, labels, or other
nonnumerical characteristics.
Quantitative data are numerical measurements that arise from a
natural numerical scale.
, The relationship between a population of interest and a sample drawn from
that population is the most important concept in statistics, since everything
else rests on it.
In our same sample of 200 cars, if 172 cars in the sample are less
than six years old, which is 0.86 or 86%, then we would estimate the
parameter of interest—the population proportion—to be about the
same as the sample statistic, the sample proportion: about 0.86.
Key Takeaways
Statistics is a study of data: describing properties of data (descriptive statistics) and
drawing conclusions about a population based on information in a sample
(inferential statistics).
The distinction between a population together with its parameters and a sample
together with its statistics is a fundamental concept in inferential statistics.
Information in a sample is used to make inferences about the population from which
the sample was drawn.
Teaching Tips
Before introducing the basic concepts of statistics, the instructor can discuss the
importance of statistics and how it has helped millions of researchers analyze and
interpret data to arrive at conclusions and understand their topic area of interest in
greater detail.
Instructors can then ask the students to come up with examples of situations where
the use of statistics would be required to arrive at specific conclusions for a particular
topic of study. The instructor can use any of these examples to explain the basic
concepts mentioned in this section.
, Alternative Examples
A group of researchers is conducting a study on the percentage of Chinese products
being consumed by U.S. consumers, in comparison to products from other countries
(including the U.S.) and their products’ quality. They want to find out if the usage of
Chinese products is increasing every year and if they are likely to completely
dominate the U.S. market in the near future.
A group of car enthusiasts wants to know what percentage of ethanol-gas mixture is
sold for consumers’ use in the U.S.
1.2 Overview
o To obtain an overview of the material in the text.
Section Outline
The example discussed in the previous section is fairly simple. However, it
illustrates some significant problems.
The sample average is an example of what is called a random variable: a
number that varies from trial to trial of an experiment.
In the example, we have supposed that the 200 cars of the sample
had an average value of $8357 (a number that is precisely known),
and concluded that the population has an average of about the same
amount, although its precise value is still unknown. However, it is
almost certain that we will get a different sample average if we take
another sample of exactly the same size from exactly the same
population.
Different samples have different levels of reliability.
