1_introduction to Statistics_June-22, 2011 [Compatibility Mode]

8/3/2019 1_introduction to Statistics_June-22, 2011 [Compatibility Mode]

1/12

Page 1

1

Quantitative Methods andBusiness Statistics for

Decision Making (MSA606)

Ramesh [email protected]

Department of Mechanical Engineering, NIT CalicutKerala, India -673 601.

Dedicated to

Professor. S. G. DeshmukhProfessor. S. G. DeshmukhProfessor. S. G. DeshmukhProfessor. S. G. Deshmukh

[email protected]

3

Objectives of this course

Appreciate the role of statistics in various decision making situations Summarize data with frequency distributions and graphic

presentation. Interpret descriptive statistics for central tendency, dispersion and

location Define and interpret probability. Utilize discrete and continuous

probability distributions to determine probabilities in variousmanagerial applications.

Apply the central limit theorem to determine probabilities of samplemeans and compute and interpret point and interval estimates.

Conduct Hypothesis tests for means Utilize linear regression to estimate and predict variables.

Understand basic concepts of design-of-experiment

Understand importance of non-parametric tests

[email protected]

Lab/tutorial

The laboratory content will require pre-

requisite of working with Excel. There willbe quizzes/assignments every week. Thelab assignments are to be submitted on

that day itself. Students will be alsorequired to visit and consult useful web

resources.

[email protected] 4

Mode of Evaluation andGrades

Grades are based on total points earned

from test 1 &2,lab/tutorial/assignments,mini-project and end semester

examination.

[email protected] 5

Test1

Article critique &

Presentation

EndSemester

Lab/tutorial/quizes

/assignments

(every week)

Mini-Project

30 % 10 % 40 % 10 % 10%

Reference

Meyer PL, Introductory Probability and StatisticalApplications, Oxford and IBH Publishers

Miller IR, Freund JE, Johnson R, Probability and

Statistics for Engineers, Prentice-Hall (I) Ltd Walpole RE and Myers RH, Probability &

Statistics for Engineers and Scientists,Macmillan

Levin, R. I. and Rubin, D.S., Statistics forManagement (Pearson Education )

[email protected] 6


2/12

Page 2

7

Statistics..

Plays an important role in many facets of

human endeavour Occurs remarkably frequently in our

everyday lives

It is often incorrectly thought of as just acollection of data, graphs and diagrams

[email protected] 8

Statistics in Business

Accounting auditing and cost estimation

Economics regional, national, and internationaleconomic performance

Finance investments and portfolio management Management human resources, compensation,

and quality management Management Information Systems (ERP):

performance of systems which gather, summarize,and disseminate information to various manageriallevels

Marketing market analysis and consumerresearch

International Business market and demographicanalysis

[email protected]

9

What is Statistics?

Science of gathering, analyzing, interpreting,and presenting data

Branch of mathematics

Facts and figures

Measurement taken on a sample

Statistics is the scientific method thatenables us to make decisions as responsiblyas possible.

[email protected] 10

Statistics

The science of data to answer researchquestions Formulate a research question(s) (hypothesis)

Collect data

Analyze and summarize data

Draw conclusions to answer researchquestions

Statistical Inference

In the presence of variation

[email protected]

11

Answers Questions from EverydayLife

Business: Will a new marketing strategy beprofitable?

Industry: Will a products life exceed the

warranty period? Medicine: Will this years flu vaccine reduce thechance of flu?

Education: Will technology improve learning?

Government: Will a change in interest ratesaffect inflation?


Statistics: Science ofvariability..?

Virtually everything varies

Variation occurs among individuals

Variation occurs within any one individualas time passes

[email protected]


3/12

Page 3

13

Can Statistics Be Trusted?There are three kinds of lies:

Lies, damned lies, and statistics.--Mark Twain

It is easy to lie with statistics. But it is

easier to lie without them.--Frederick Mosteller

Figures wont lie but liars will figure.--Charles Grosvenor


Population Versus Sample Population the whole

a collection of persons, objects, or items under study

The entire group of individuals in a statistical study wewant information about.

Census gathering data from the entirepopulation

Sample a portion of the whole a subset of the population a part of the population from which we actually collect

information, used to draw conclusions about thewhole (statistical inference

[email protected]

15

Statistics can be split into twobroad categories

1. Descriptive statistics

2. Statistical inference

[email protected]

Descriptive Statistics

Collect data

ex. Survey

Present data

ex. Tables and graphs

Characterize data

ex. Sample mean =i

X

n

17

Descriptive statistics..

Encompasses the following:

Graphical or pictorial display

Condensation of large masses of data into a

form such as tables

Preparation of summary measures to give aconcise description of complex information(e.g. an average figure)

Exhibition of patterns that may be found insets of information

[email protected]

Inferential Statistics

Estimation

ex. Estimate thepopulation mean weight

using the sample meanweight

Hypothesis testing

ex. Test the claim that thepopulation mean weightis 120 poundsDrawing conclusions and/or making decisions

concerning a population based on sample results.


4/12

Page 4

19

Inferential Statistics..

Especially relates to:

Determining whether characteristics of asituation are unusual or if they havehappened by chance

Estimating values of numerical quantities anddetermining the reliability of those estimates

Using past occurrences to attempt to predictthe future


Process of Inferential Statistics

Population

(parameter)

Sample

x

(statistic )

Calculate xto estimate

Select a

random sample

[email protected]

Population vs. Sample

Population Sample

Measures used to describe the

population are called parameters

Measures computed from

sample data are called statistics22

Parameter vs. Statistic

Parameter descriptive measure of thepopulation

Usually represented by Greek letters

Statistic descriptive measure of asample

Usually represented by Roman letters

[email protected]

23

Symbols for PopulationParameters

denotes population parameter

2

denotes population variance denotes population standard deviation


Symbols for Sample Statistics

x denotes sample mean

2S denotes sample variance

S denotes sample standard deviatio

[email protected]


5/12

Page 5

Types of Variables

Categorical (qualitative) variables have values

that can only be placed into categories, such asyes and no.

Numerical (quantitative) variables have values

that represent quantities.

Types of Variables

Data

Categorical Numerical

Discrete Continuous

Examples:

Marital Status

Political Party Eye Color

(Defined categories)Examples:

Number of Children

Defects per hour

(Counted items)

Examples:

Weight

Voltage

(Measured characteristics)

27

Levels of Data Measurement

Nominal Lowest level of measurement

Ordinal

Interval

Ratio Highest level of measurement

[email protected]

Levels of Measurement

A nominal scale classifies data into distinct

categories in which no ranking is implied.

Categorical Variables Categories

Personal ComputerOwnership

Type of Stocks Owned

Internet Provider

Yes/ No

Microsoft Network / AOL

Growth Value Other


An ordinal scale classifies data into distinct

categories in which ranking is implied

Categorical Variable Ordered Categories

Student c lass des igna tion Freshman, Sophomore , Junio r,Senior

Product satisfaction Satisfied, N eutral, Unsatisfied

Faculty rank Professor, Associate Professor,Assistant Professor, Instructor

Standard & Poors bond ratings AAA, AA, A, BBB, BB, B, CCC, CC,

C, DDD, DD, D

Student Grades A, B, C, D, F


An interval scale is an ordered scale in which thedifference between measurements is a meaningfulquantity but the measurements do not have a true

zero point.

A ratio scale is an ordered scale in which thedifference between the measurements is ameaningful quantity and the measurements have a

true zero point.


6/12

Page 6

Interval and Ratio Scales

32

Usage Potential of VariousLevels of Data

Nominal

Ordinal

IntervalRatio

[email protected]

33

Data Level, Operations,and Statistical Methods

Data Level

Nominal

Ordinal

Interval

Ratio

Meaningful Operations

Classifying and Counting

All of the above plus Ranking

All of the above plus Addition,Subtraction

All of the above plusmultiplication and division

StatisticalMethods

Nonparametric

Nonparametric

Parametric

Parametric


Data preparation rules

Data presented must be

factual

relevant

Before presentation always check:

the source of the data

that the data has been accurately

transcribed

the figures are relevant to the problem

[email protected]

35

Methods of visual presentationof data

Table

1st Qtr 2nd Qtr 3rd Qtr 4th QtrEast 20.4 27.4 90 20.4

West 30.6 38.6 34.6 31.6

North 45.9 46.9 45 43.9



Graphs

0

10

20

30

40

50

6070

80

90

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

East

West

North

[email protected]


7/12

Page 7

37


Pie chart

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr



Multiple bar chart

0 20 40 60 80 100

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

North

West

East

[email protected]

39


Simple pictogram

0

20

40

60

80

100

1 st Q tr 2 nd Q tr 3 rd Q tr 4 th Q tr

East

North

West


Frequency distributions

Frequency tables

ClassInterval Frequency Cumulative Frequency

< 20 13 13


8/12

Page 8

43

Example of UngroupedData

4230

53

50

52

30

55

49

61

74

2658

40

40

28

36

30

33

31

37

3237

30

32

23

32

58

43

30

29

3450

47

31

35

26

64

46

40

43

5730

49

40

25

50

52

32

60

54

Ages of a Sample of

Managers from

XYZ


Frequency Distribution ofAges

Class Interval Frequency20-under 30 6

30-under 40 18

40-under 50 11

50-under 60 11

60-under 70 3

70-under 80 1

[email protected]

45

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

Smallest

Largest

Range = Largest - Smallest

= 74 - 23

= 51


Number of Classes and ClassWidth

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 anapproximate class width

Round up to a convenient number

10=WidthClass

8.5=6

51=WidthClasseApproximat

[email protected]

47

Class Midpoint

Class Midpoint =beginning class endpoint + ending class endpoint

2

= 30 + 402

= 35

( )

Class Midpoint = class beginning point +1

2class width

= 30 +1

210

= 35


Relative FrequencyRelative

Class 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=

18

50=

[email protected]


9/12

Page 9

49

Cumulative Frequency

Cumulative

Class Interval Frequency Frequency20-under 30 6 6

30-under 40 18 24

40-under 50 11 35

50-under 60 11 46

60-under 70 3 49

70-under 80 1 50

Total 50

18 + 6

11 + 24


Class Midpoints, Relative Frequencies,

and Cumulative Frequencies

Relative Cumulative

Class IntervalFrequency Midpoint Frequency Frequency

20-under 30 6 25 .12 6

30-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 [email protected]

51

Cumulative Relative Frequencies

Relative Cumulative Cumulative Relative

Class IntervalFrequencyFrequencyFrequency Frequency

20-under 30 6 .12 6 .12

30-under 40 18 .36 24 .48

40-under 50 11 .22 35 .70

50-under 60 11 .22 46 .92

60-under 70 3 .06 49 .98

70-under 80 1 .02 50 1.00

Total 50 [email protected] 52

Common Statistical Graphs

Histogram -- vertical bar chart of frequencies

Frequency Polygon -- line graph of frequencies

Ogive -- line graph of cumulative frequencies

Pie Chart -- proportional representation forcategories of a whole

Stem and Leaf Plot

Pareto Chart

Scatter Plot

[email protected]

53

Histogram

Class Interval Frequency

20-under 30 6

30-under 40 1840-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


Histogram Construction


20-under 30 6

30-under 40 1840-under 50 11

50-under 60 11

60-under 70 3

70-under 80 10

10

20

0 10 20 30 40 50 60 70 80

Years

Frequency

[email protected]


10/12

Page 10

55

Frequency Polygon

Class Interval Frequency20-under 30 6

30-under 40 18

40-under 50 11

50-under 60 11

60-under 70 3

70-under 80 10

10

20

0 1 0 20 3 0 4 0 5 0 60 7 0 8 0

Years

Frequency


Ogive

Cumulative


20-under 30 6

30-under 40 24

40-under 50 35

50-under 60 46

60-under 70 49

70-under 80 500

20

40

60

0 10 20 30 40 50 60 70 80

Years

Frequency

[email protected]

57

Relative Frequency Ogive

Cumulative

Relative


20-under 30 .12

30-under 40 .48

40-under 50 .70

50-under 60 .92

60-under 70 .98

70-under 80 1.00

0.000.100.200.300.400.500.600.700.800.901.00

0 10 20 30 40 50 60 70 80

Years

CumulativeRelativeFrequency


Complaints by Passengers

COMPLAINT NUMBER 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 [email protected]

59

Complaints by Passengers

Stations, Etc.

40%Train

Performance

21%

Equipment15%

Personnel

14%

Schedules,

Etc.

10%


SecondQuarter Truck

Production

2d QuarterTruck

ProductionCompany

A

B

C

D

ETotals

357,411

354,936

160,997

34,099

12,747920,190

[email protected]


11/12

Page 11

61

39%

39%

17%

4%1%

A B C D E

Second QuarterTruck Production


Pie Chart Calculations forCompany A

2d Quarter

TruckProduction

Proportion DegreesCompany

A

B

C

D

ETotals

357,411

354,936

160,997

34,099

12,747920,190

.388

.386

.175

.037

.0141.000

140

139

63

13

5360

357,411

920,190=

. 388 360 =

[email protected]

63

Pareto Chart

0

10

20

30

40

50

60

70

80

90

100

Poor

Wiring

Short in

Coil

Defective

Plug

Other

Frequency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%


Scatter Plot

RegisteredVehicles(1000's)

Gasoline Sales(1000's ofGallons)

5 60

15 120

9 90

15 140

7 60

0

100

200

0 5 10 15 20RegisteredVehicles

GasolineSales

[email protected]

Principles of Excellent Graphs

The graph should not distort the data.

The graph should not contain unnecessary

adornments (sometimes referred to as chart junk).

The scale on the vertical axis should begin at zero.

All axes should be properly labeled.

The graph should contain a title.

The simplest possible graph should be used for a

given set of data.

Graphical Errors: Chart Junk

1960: $1.00

1970: $1.60

1980: $3.10

1990: $3.80

Minimum Wage

Bad Presentation

Minimum Wage

0

2

4

1960 1970 1980 1990

$

Good Presentation


12/12

Page 12

Graphical Errors:Compressing the Vertical Axis

Good PresentationQuarterly Sales Quarterly Sales

Bad Presentation

0

25

50

Q1 Q2 Q3 Q4

$

0

100

200

Q1 Q2 Q3 Q4

$

Graphical Errors: No Zero Pointon the Vertical Axis

Monthly Sales

36

39

42

45

J F M A M J

$

Graphing the first six months of sales

Monthly Sales

0

39

42

45

J F M A M J

$

36

Good PresentationsBad Presentation

69

Thank You

http://www.stats.gla.ac.uk/steps/glossary/p

resenting_data.html

http://www.ilir.uiuc.edu/courses/lir593/

1_introduction to Statistics_June-22, 2011 [Compatibility Mode]

Documents

Transcript of 1_introduction to Statistics_June-22, 2011 [Compatibility Mode]