Business Stats Basic

8/10/2019 Business Stats Basic

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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 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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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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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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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.
http://en.wikipedia.org/wiki/Cartesian_coordinateshttp://en.wikipedia.org/wiki/Cartesian_coordinates


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Histogram


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


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


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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Business Stats Basic

Documents

Transcript of Business Stats Basic