Transcript Statistics

Chapter 1
Introduction to the statistics
Chapter One
What is Statistics?
GOALS
When you have completed this chapter, you will be able to:
ONE
Understand why we study statistics.
TWO
Explain what is meant by descriptive statistics and inferential statistics.
THREE
Distinguish between a qualitative variable and a quantitative variable.
FOUR
Distinguish between a discrete variable and a continuous variable.
FIVE
Distinguish among the nominal, ordinal, interval, and ratio levels
of measurement.
SIX
Define the terms mutually exclusive and exhaustive.
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History of statistics
• The history of statistics can be said to start around
1749 although, over time, there have been changes to
the interpretation of what the word statistics means. In
early times, the meaning was restricted to information
about states. This was later extended to include all
collections of information of all types, and later still it was
extended to include the analysis and interpretation of
such data. In modern terms, "statistics" means both sets
of collected information, as in national accounts and
temperature records, and analytical work which requires
statistical inference.
History of statistics
• Statistical activities are often associated with models
expressed using probabilities, and require probability
theory for them to be put on a firm theoretical basis: see
History of probability.
• A number of statistical concepts have had an important
impact on a wide range of sciences. These include the
design of experiments and approaches to statistical
inference such as Bayesian inference, each of which can
be considered to have their own sequence in the
development of the ideas underlying modern statistics.
• Contents
Why study statistics?
• Numerical info is everywhere
– But how do we know if conclusions reported are
accurate?
• Statistical techniques are used to make
decisions that affect our lives
– This is why younger people pay more for insurance…
• Knowledge of statistical methods at least helps
you understand why decisions are made
– In future you will make decisions that involve data
What is Meant by Statistics?
In common usage statistics refers to numerical
information….. But in this course the term has a
wider meaning….
•
Statistics is the science of
collecting, organizing,
presenting, analyzing, and
interpreting numerical data to
assist in making more
effective decisions.
Who Uses Statistics?
•
Statistical techniques are used
extensively by managers in
marketing, accounting, quality
control, consumers, professional
sports people, hospital
administrators, educators,
politicians, physicians, gamblers,
etc...
Types of Statistics
•
Descriptive Statistics: Methods of
organizing, summarizing, and
presenting data in an informative way.
EXAMPLE
1: A Gallup poll found that 49% of
the people in a survey knew the name of the first
book of the Bible. The statistic 49 describes the
number out of every 100 persons who knew the
answer.
Types of Statistics
•
Descriptive Statistics: Methods of
organizing, summarizing, and
presenting data in an informative way.
EXAMPLE 2: According to Consumer Reports,
General Electric washing machine owners reported
9 problems per 100 machines during 2002. The
statistic 9 describes the number of problems out of
every 100 machines.
Types of Statistics
•
Descriptive Statistics: Methods of
organizing, summarizing, and
presenting data in an informative way.
EXAMPLE 3: The Canadian government reports
that the population of Canada was 18,238,000 in
1961, 21,568,000 in 1971, 24,820,000 in 1981,
28,031,000 in 1991, and 31,050,700 in 2001. If we
calculate percentage growth over the decades it is
also descriptive statistics.
Types of Statistics
•
Inferential Statistics: The
methods used to determine
something about a population,
based on a sample.
O EXAMPLE 1: In the preceding example on
Canadian population changes, if you use the
past data to forecast the population of Canada
in the year 2010 or expected percentage of
growth from 2000 to 2010, then this is
considered inferential statistics.
Types of Statistics
•
Inferential Statistics: The
methods used to determine
something about a population,
based on a sample.
EXAMPLE
2: The accounting department of a
large firm will select a sample of the invoices to
check for accuracy for all the invoices of the
company.
Types of Statistics
•
Inferential Statistics: The
methods used to determine
something about a population,
based on a sample.
EXAMPLE
3: Wine tasters sip a few drops of
wine to make a decision with respect to all the
wine waiting to be released for sale.
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Population vs. Sample
Population is the entire set of
individuals or objects of interest or the
measurements obtained from all
individuals or objects of interest.
Sample is a portion, or part, of the
population of interest
Population: All items
Sample: Items selected from the population
See also p.7
• NB: don’t confuse population in statistics
with a country’s population!
• A population might consist of all the
people in Nanaimo but also may mean the
PE ratios for all chemical stocks, or total
assets of the 20 largest banks in North
America, total collection of prices, ages,
square footage of retail space in Nanaimo,
and so on.
Types of Variables
•
For a Qualitative or Attribute
variable the characteristic being
studied is nonnumeric.
EXAMPLES:
Gender, religious affiliation,
type of automobile owned, country of birth,
eye colour are examples.
Types of Variables
•
•
In a Quantitative variable
information is reported numerically.
EXAMPLES:
balance in your chequing
account, minutes remaining in class, or
number of children in a family.
Types of Variables
•
Quantitative variables can be classified
as either discrete or continuous.
•
•Discrete variables: can only assume certain values
and there are usually “gaps” between values.
EXAMPLE:
the number of bedrooms in a
house, or the number of hammers sold at the local
Home Depot (1,2,3,…,etc). But you cannot have
2.3 bedrooms or 10.6 hammers…Thus discrete
variables result from counting.
Types of Variables
•
•
A continuous variable can assume
any value within a specified range.
Examples are: The pressure in a tire,
the weight of a pork chop, or the height
of students in a class. Typically,
continuous variables are the result
of measuring something.
Summary of Types of Variables
DATA
Qualitative or attribute
(type of car owned)
Quantitative or numerical
discrete
(number of children)
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continuous
(time taken for an exam)
Thanks for Your Attention