Transcript Chapter 1

What is Statistics
Chapter 1
McGraw-Hill/Irwin
©The McGraw-Hill Companies, Inc. 2008
GOALS
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What is meant by statistics?
Understand why we study statistics.
Explain what is meant by descriptive statistics and
inferential statistics.
Distinguish between a qualitative variable and a
quantitative variable.
Describe how a discrete variable is different from a
continuous variable.
Distinguish among the nominal, ordinal, interval, and
ratio levels of measurement.
What Is Meant By Statistics?
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Common meaning:
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Numerical information such as:
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Mean time waiting on hold for technical support is 17
minutes
In a recent poll, 21% of respondents approved of the
President’s policies
Statistic: One figure
Statistics: more than one figure
What Is Meant By Statistics?
Statistics is interested in what is a typical value
and how much variation there is in the data
Typical value:
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Variation
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Some sort of average (Mean, Median, Mode)
How reliable is the average
How clustered are the data points around the mean
What is Meant by Statistics?
Statistics is the science of
collecting, organizing, presenting,
analyzing, and interpreting
numerical data to assist in making
more effective decisions.
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Understand why we study statistics
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Because numeric and non-numeric data are
everywhere
In marketing, accounting, finance,
economics, politics, sciences, and
elsewhere, there are statistics
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We need to be able to understand statistics when
we encounter them
We need to not be tricked by misleading statistics
We need to use statistics to help us make
decisions under future uncertainty
Who Uses Statistics?
Statistical techniques are used
extensively by marketing,
accounting, quality control,
consumers, professional sports
people, hospital administrators,
educators, politicians, physicians,
etc...
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Types of Statistics – Descriptive
Statistics
Descriptive Statistics - methods of
organizing, summarizing, and
presenting data in an informative
way.
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Descriptive Statistics
EXAMPLE 2: According
to Consumer Reports,
General Electric
washing machine
owners reported 9
problems per 100
machines during
2001. The statistic 9
describes the number
of problems out of
every 100 machines.
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Descriptive Statistics
18.50%
6.50%
4.50%
Nike
Adidas
Reebok
Asics
Other
24.50%
46%
EXAMPLE 3: Pie Chart (chapter 2) For Running
Shoes Sold At Big 5 Sports
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Descriptive Statistics
Frequency Distribution of Selling Prices
at Whitner Pontiac Last Month
Selling Prices
($ thousands)
12 up to 15
15 up to 18
18 up to 21
21 up to 24
24 up to 27
27 up to 30
30 up to 33
Total
Number of
Vehicles Sold
(Frequency)
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18
8
4
2
80
EXAMPLE 4: Frequency Distribution (chapter 2)
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Types of Statistics – Descriptive
Statistics
 Inferential
Statistics definition 1: The
methods used to estimate a
property of a population on the basis
of a sample.
 Inferential Statistics definition 2: A
decision, estimate, prediction, or
generalization about a population,
based on a sample.
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Population versus Sample
A population is a collection of all possible individuals, objects, or
measurements of interest.
A sample is a portion, or part, of the population of interest
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Inferential Statistics
Example 1: TV networks
constantly monitor
the popularity of their
programs by hiring
Nielsen and other
organizations to
sample the
preferences of TV
viewers.
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#1
Inferential Statistics
Example 2: 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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Example 3: 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.
Descriptive Statistics Or Inferential
Statistics?
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There are a total of 42,796 miles of interstate
highways in the United States
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Auditors take a sample of a firm’s invoices in
order to assess the magnitude of reliability of
the accounting invoicing system
Types of Variables
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Qualitative or Attribute variable - the
characteristic being studied is
nonnumeric.
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EXAMPLES: Gender, type of automobile owned,
state of birth, eye color are examples.
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Qualitative data are usually summarized in
graphs or bar charts
(Nominal or ordinal level of measurement)
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Types of Variables
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Quantitative variable - information is
reported numerically.
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EXAMPLES: balance in your checking account,
minutes remaining in class, or number of children in a
family.
 Quantitative
variables can be
classified as either Discrete or
Continuous.
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Quantitative Variables - Classifications
 Discrete
variables: can only assume
certain values and there are usually
“gaps” between values.
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EXAMPLE: the number of bedrooms in a house, or the number of
hammers sold at the local Home Depot (1,2,3,…,etc).
Quantitative Variables - Classifications
 Continuous
variable can assume any
value within a specified range.
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EXAMPLE: The pressure in a tire, the weight of a pork chop, or
the height of students in a class.
Usually is measured (accuracy depends on measuring
instrument)
Money is often categorized as a continuous variable (even though
you can’t count between pennies)
Distinguish Between A Qualitative Variable
And A Quantitative Variable
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Colors of M & M candies?
Amount of money in your retirement
account?
Score on test?
Type of bike you own?
Summary of Types of Variables
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Four Levels of Measurement
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Levels of measurement dictate:
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The calculations that can be done to summarize & present the
data
The statistical tests that can be preformed
level – No order
 Ordinal level – Order but no set distance between
 Nominal
levels
 Interval
level - Order with set distances between
levels, zero just a point on the scale, no division
 Ratio
level - Order with set distances between levels,
inherent zero starting point, division OK
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Nominal Level
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Nominal level - data that is classified into
categories and cannot be arranged in any particular
order.
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Observations of a qualitative variable can only be
classified and counted. There is no particular order
to the labels.
Nominal level properties:
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2.
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EXAMPLES: Eye color, gender, car make
Data categories are represented by labels or names.
Even when the labels are numerically coded, the data
categories have no logical order.
# unemployed/100,000
Nominal Level
10000
8900
8900
9000
8200
8000 7300
6700
7000
5400
6000
5000
4000
3000
2000
1000
0
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2
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Atlanta
Boston
Chicago
Los Angeles
New York
Washington
6
Cities
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Ordinal Level
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Ordinal level – involves data arranged in some
order, but the differences between data values
cannot be determined or are meaningless.
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Ordinal level properties:
1.
2.
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EXAMPLE: During a taste test of 4 soft drinks, Mellow Yellow
was ranked number 1, Sprite number 2, Seven-up number 3,
and Orange Crush number 4.
EXAMPLE: How do you rate your instructor?
EXAMPLE: Order of finish in race.
Data classifications are represented by sets of labels or
names (high, medium, low or very good, good, poor) that
have relative values.
Because of the relative values, the classified data can be
ranked or ordered.
Ordinal Level
During a taste test
of 4 soft drinks,
Coca Cola was
ranked number 1,
Dr. Pepper number
2, Pepsi number 3,
and Root Beer
number 4.
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2
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3
Interval Level
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Interval level:
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One category is higher than
another (Ordered).
There is a constant unit of
measurement.
Zero is just a point on the
scale; or there is no natural
zero point.
Division of two numbers does
not make sense.
Scale or rank are good
examples
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EXAMPLE: Temperature on
the Fahrenheit scale.
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EXAMPLE: Shoe size and
dress size.
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There is no natural zero point
EXAMPLE: Years in which
Whole Foods Market Inc. stock
split.
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Zero is just a point on the
scale.
Division of 1992 and 1993
does not make sense.
EXAMPLES: Rank of Indi 500
results, Test scores.
Interval Level
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Interval level properties:
1.
2.
Data classifications are ordered according to the
amount of the characteristic they possess.
Equal differences in the characteristic are
represented by equal differences in the
measurement.
1.
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The increment amount up or down is always the same.
Ratio Level
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Ratio level - the interval level with an
inherent zero starting point. Differences and
ratios are meaningful for this level of
measurement.
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Practically all quantitative data are the ratio level
of measurement.
EXAMPLES: Monthly income of surgeons,
distance traveled by Sales Rep. per month, Bank
account amount, weight, height, wages, units of
production….
Ratio Level
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Bank account dollars
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Zero is not just a point on the scale, it is the
inherent starting point.
Zero means that you don’t have any money.
Zero means that there is a complete absence of
money.
Division has meaning:
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Starting balance = $1000.
Ending balance = $1500.
Decimal equivalent change = 1500/1000-1 = .50.
Ratio Level
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Ratio level properties:
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Data classifications are ordered according to the
amount of the characteristics they posses.
Equal differences in the characteristics are
represented by equal differences in the number
assigned to the classification.
The zero point is the absence of the
characteristic and the ratio between two
numbers is meaningful.
Summary of the Characteristics for
Levels of Measurement (example 1)
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Summary of the Characteristics for
Levels of Measurement (example 2)
Levels of Data
Nominal
Data may only
be classified
(no order)
1.
2.
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Jersey #
Make of car
Ordinal
Interval
Ratio
Meaningful 0 point
Data are ranked
Meaningful
differences
between values
1.
2.
Team standings
in the Pac 10
CPA exam rank
1.
2.
3.
Temperature
Shoe size
Score on Test
& ratio
between values
1.
2.
Checkbook Bal.
Stock values
End of Chapter 1
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