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Business statistics
Session 1
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Learning Objectives
Define statistics.
Become aware of a wide range ofapplications of statistics in business.
Differentiate between descriptive andinferential statistics.
Classify numbers by level of data andunderstand why doing so is important whydoing so is important .
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Statistics in Business
Accounting auditing and cost estimation
Economics regional, national, and international economicperformance
Finance investments and portfolio management
Management human resources, compensation, andquality management
Management Information Systems performance ofsystems which gather, summarize, and disseminateinformation to various managerial levels
Marketing market analysis and consumer research
International Business market and demographic analysis
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What is Statistics?
Science of gathering, analyzing,interpreting, and presenting data onvarious topics
Branch of mathematics Course of study
Facts and figures
Measurement taken on a sample Type of distribution being used to analyze
data
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Statistics in Business
Statistics science dealing with thecollection, analysis, interpretation, andpresentation of numerical data
Branches of statistics Descriptive using data gathered on a group
to describe or reach conclusions about thegroup.
Inferential data gathered from a sample and
used to reach conclusions about the populationfrom which the data was gathered
Used to draw conclusions about the group orsimilar groups
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Population
Population of cars
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Population and Census Data
Identifier Color MPG
RD1 Red 12
RD2 Red 10
RD3 Red 13RD4 Red 10
RD5 Red 13
BL1 Blue 27
BL2 Blue 24
GR1 Green 35
GR2 Green 35
GY1 Gray 15
GY2 Gray 18
GY3 Gray 17
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Sample and Sample Data
Sample of cars
Identifier Color MPG
RD2 Red 10
RD5 Red 13
GR1 Green 35
GY2 Gray 18
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Parameter vs. Statistic
Parameter descriptivemeasure of the population
Usually represented by Greekletters
Statistic descriptive measure
of a sample Usually represented by Roman
letters
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Symbols for Population Parameters
Most commonly used symbols are:
parameterpopulationdenotes2
denotes population variance
denotes population standard deviatio
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Symbols for Sample Statistics
meansampledenotesx2
S denotes sample variance
Sdenotes sample standard deviatio
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Process of Inferential Statistics
)(parameter
Population1.
)(statistic
xSample3.
estimateto
xCalculate4.
samplerandom
aSelect2.
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Statistics in Business
Difference between a parameter andstatistic is only important in the useof inferential statistics
Calculations of parameter can be costprohibitive
When cost prohibitive, a sample calculatesappropriate statistics.
Researchers use the calculation as anestimate of the parameter.
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Levels of Data Measurement
Nominal In nominal measurementthe numerical values just "name" theattribute uniquely.
No ordering of the cases is implied. Forexample, jersey numbers in basketballare measures at the nominal level.
A player with number 30 is not more of
anything than a player with number 15,and is certainly not twice whatevernumber 15 is.
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Levels of Data Measurement
Ordinal - A variable is ordinalmeasurable if ranking is possible forvalues of the variable.
For example, a gold medal reflectssuperior performance to a silver orbronze medal in the Olympics, or youmay prefer French toast to waffles, andwaffles to oat bran muffins.
First, Second are ordinalmeasurements.
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Levels of Data Measurement
Ratio in ratio measurement there isalways an absolute zero that ismeaningful.
This means that you can construct ameaningful fraction (or ratio ) with aratio variable.
In applied social research most "count"
variables are ratio, for example, thenumber of clients in past six months.
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Nominal Level Data
Numbers are used to classify orcategorize
Example: Employment Classification
1 for Educator
2 for Construction Worker
3 for Manufacturing Worker
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Ordinal Level Data
Numbers are used to indicate rank or order Relative magnitude of numbers is meaningful Differences between numbers are not
comparable
Example: Ranking productivity ofemployeesExample: Position within an organization 1 for President 2 for Vice President 3 for Plant Manager 4 for Department Supervisor 5 for Employee
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Ordinal Data
Faculty and staff should receivepreferential treatment for parkingspace.
1 2 3 4 5
StronglyAgree
Agree StronglyDisagree
DisagreeNeutral
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Interval Level Data
Interval Level data - Distances betweenconsecutive integers are equal Relative magnitude of numbers is meaningful
Differences between numbers are comparable
Location of origin, zero, is arbitrary
Vertical intercept of unit of measure transformfunction is not zero (Y=b+aX).
Example: Fahrenheit Temperature=32+9/5Centigrade
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Ratio Level Data
Highest level of measurement
Relative magnitude of numbers is meaningful
Differences between numbers are comparable
Location of origin, zero, is absolute (natural)
Vertical intercept of unit of measure transformfunction is zero (Y=aX).
Statistician can create ratios with data.
Examples: Height, Weight, and Volume
Example: Monetary Variables, such as Profit andLoss, Revenues, Expenses, Financial ratios - such asP/E Ratio, Inventory Turnover, and Quick Ratio.
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Categories of statistical techniques
Parametric statistics requires that the databe interval or ratio(metric data orquantitative).
Non Parametric used if data are nominal orordinal(nonmetric or qualitative)
Non parametric statistics can be used toanalyze interval or ratio data.
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Data Level, Operations, andStatistical Methods
Data Level Meaningful OperationsStatisticalMethods
Nominal
Ordinal
Interval
Ratio
Classifying and counting
All of the above plus ranking
All of the above plus addition,subtraction, multiplication
and division
Almost all operations
Nonparametric
Nonparametric
Parametric
Parametric
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Part II:Charts and Graphs
Learning Objectives
Recognize the difference between
grouped and ungrouped data Construct a frequency distribution
Construct a histogram, a frequencypolygon, an ogive, a pie chart, a stemand leaf plot and a scatter plot
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Ungrouped Versus Grouped Data
Ungrouped data
have not been summarized in any way
are also called raw data
Grouped data
have been organized into a frequencydistribution
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Example of Ungrouped Data
42
30
53
50
52
30
55
49
61
74
26
58
40
40
28
36
30
33
31
37
32
37
30
32
23
32
58
43
30
29
34
50
47
31
35
26
64
46
40
43
57
30
49
40
25
50
52
32
60
54
Ages of a Sample of
Managers from
Urban Child Care
Centers in the
United States
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Frequency Distribution
Frequency Distribution summary ofdata presented in the form of classintervals and frequencies
Vary in shape and design
Constructed according to the individualresearcher's preferences
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Frequency Distribution
Steps in Frequency Distribution Step 1 - Determine range of frequency
distribution
Range is the difference between the high and
the lowest numbers Step 2 determine the number of classes
Dont use too many, or two few classes
Step 3 Determine the width of the classinterval
Approx class width can be calculated bydividing the range by the number of classes.
Values fit into only one class
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Frequency Distribution of ChildCare Managers Ages
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
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Data Range
42
30
53
50
52
30
55
49
61
74
26
58
40
40
28
36
30
33
31
37
32
37
30
32
23
32
58
43
30
29
34
50
47
31
35
26
64
46
40
43
57
30
49
40
25
50
52
32
60
54
Range = Largest - Smallest
= 74 - 23
= 51
smallest
Largest
Smallest
largest
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Number of Classes and Class Width
The number of classes should be between 5 and 15.
Fewer than 5 classes cause excessive summarization.
More than 15 classes leave too much detail.
Class Width Divide the range by the number of classes for an
approximate class width
Round up to a convenient number
10=WidthClass
8.5=6
51=WidthClasseApproximat
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Class Midpoint
The midpoint of each class interval is called theclass midpoint or the class mark.
Class Midpoint =beginning class endpoint + ending class endpoint
2
=30 + 40
2
= 35
Class Midpoint = class beginning point +1
2class width
= 30 +1
210
= 35
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Relative Frequency The relative frequency is the proportion of the total frequency
in any given class interval in a frequency distribution.
18
50
RelativeClass Interval Frequency Frequency
20-under 30 6 .12
30-under 40 18 .36
40-under 50 11 .22
50-under 60 11 .22
60-under 70 3 .06
70-under 80 1 .02
Total 50 1.00
6
50
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Cumulative Frequency
The cumulative frequency is a running total offrequencies through the classes of a frequencydistribution.
Class Interval Frequency Cumulative Freq0-under 30 6 6
30-under 40 18 24
40-under 50 11 35
50-under 60 11 46
60-under 70 3 4970-under 80 1 50
Total 50
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Relative Frequency
Relative frequency is the proportion of thetotal frequency that is in any given classinterval in a frequency distribution
Relative frequency = individual class frequencydivided by the total frequency
Example => Frequency/Total = 16/40 =.40
Probability of occurrence
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Cumulative Frequency
Cumulative frequency the runningtotal of frequencies through theclasses of a frequency distribution
Cumulative frequency for each class isthe frequency for that class intervaladded to the preceding cumulative total
At the last interval, the cumulative totalequals the sum of the frequencies
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Class Midpoints, Relative Frequencies,and Cumulative Frequencies
Class Interval Frequency Midpoint Relative freq Cum.freq
20-under 30 6 25 .12 630-under 40 18 35 .36 24
40-under 50 11 45 .22 35
50-under 60 11 55 .22 46
60-under 70 3 65 .06 49
70-under 80 1 75 .02 50
Total 50 1.00
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Common Statistical Graphs
Stem and Leaf Plot -- display is a graphical methodof displaying data. It is particularly useful when yourdata are not too numerous.
Scatter Plot-- type of display using Cartesiancoordinates todisplay values for two variables for a set of data.
The data is displayed as a collection of points, each having thevalue of one variable determining the position on the horizontalaxis and the value of the other variable determining theposition on the vertical axis.A scatter plot is also called a scatter chart, scatter diagram
and scatter graph.
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Histogram
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
0
10
20
0 10 20 30 40 50 60 70 80
Years
Frequency
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Histogram Construction
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
0
10
20
0 10 20 30 40 50 60 70 80
Years
Frequency
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Frequency Polygon
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
0
10
20
0 10 20 30 40 50 60 70 80
Years
Frequency
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Ogive
Cumulative
Class Interval Frequency20-under 30 630-under 40 2440-under 50 35
50-under 60 4660-under 70 4970-under 80 50
0
20
40
60
0 10 20 30 40 50 60 70 80
Years
Frequenc
y
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Complaints by Amtrak Passengers
COMPLAINT NUMBE
R
PROPORTION DEGREES
Stations, etc. 28,000 .40 144.0
TrainPerformance
14,700 .21 75.6
Equipment 10,500 .15 50.4
Personnel 9,800 .14 50.6
Schedules,
etc.
7,000 .10 36.0
Total 70,000 1.00 360.0
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Complaints by Amtrak Passengers
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Second Quarter U.S. TruckProduction
Second Quarter TruckProduction in the U.S.(Hypothetical values)
2dQuarterTruck
Production
Company
A
B
C
D
E
Totals
357,411
354,936
160,997
34,099
12,747
920,190
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Second Quarter U.S. TruckProduction
39%
17%
4%1%
39%
A B C D E
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Pie Chart Calculations for CompanyA
2d QuarterTruck
ProductionProportion DegreesCompany
A
B
C
D
E
Totals
357,411
354,936
160,997
34,099
12,747
920,190
.388
.386
.175
.037
.014
1.000
140
139
63
13
5
360
357,11/920,190
.388*360
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Safety Examination Scoresfor Plant Trainees
86
76
23
77
81
79
68
77
92
59
68
75
83
49
91
47
72
82
74
70
56
60
88
75
97
39
78
94
55
67
83
89
67
91
81
Raw Data
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Construction of Stem and Leaf Plot
86
76
23
77
81
79
68
77
92
59
68
75
83
49
91
47
72
82
74
70
56
60
88
75
97
39
78
94
55
67
83
89
67
91
81
Raw Data
Stem
Stem
Leaf
Leaf
2
3
4
5
6
7
8
9
3
9
7 9
5 6 9
0 7 7 8 8
0 2 4 5 5 6 7 7 8 9
1 1 2 3 3 6 8 9
1 1 2 4 7
Stem Leaf
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Scatter Plot
RegisteredVehicles
(1000's)
Gasoline Sales(1000's of
Gallons)
5 60
15 120
9 90
15 140
7 60
0
100
200
0 5 10 15 20Registered Vehicles
GasolineSales
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