basic elementary

7/31/2019 Basic Elementary

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MEL761: Statistics for DecisionMaking

Web site for the course:http://paniit.iitd.ac.in/~deshmukh/

Dr S G DeshmukhMechanical DepartmentIndian Institute of Technology

About the courseIntroduction

Need Descriptive and

Inferential Statistics Examples Various Problem

Areas
http://paniit.iitd.ac.in/~deshmukh/http://paniit.iitd.ac.in/~deshmukh/


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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 continuousprobability 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


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Course coverage Introduction to statistics: definitions and terminology; data classification;

data collection techniques, various scales for measurement and their relevance

Descriptive statistics: frequency distributions; measures of central tendency,Variation, Probability: basic concepts; multiplication and addition rules,Bayes rule,

Discrete probability distributions: basic concepts; Binomial , Poisson andother discrete distributions Continuous probability distributions :Exponential and other distributions:

Normal probability distributions: introductory concepts; the standard normalDistribution; central limit theorem, applications of normal distributions,approximations to discrete probability distributions

Correlation and Regression analysis: overview of correlation; linear regression

Type I and Type II errors, Confidence intervals: confidence intervals for themean (large samples and small samples) and for population proportions

Analysis of Variance and Design of Experiments, Non-parametric tests Case studies and applications to managerial decision making


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Evaluation scheme

Surprise Quizzes (n numbers) 5 % Minors(2) 30 %

Major 35% Lab work /assignments 15 % Mini-Project 10 %

Statistics application review 5 %


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Learning Objectives

Define statistics Become aware of a wide range of

applications of statistics in business for decision making

Differentiate between descriptive andinferential statistics

Formulate and test various sets of hypotheses

Understand implications of design of experiments


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Statistics..

Plays an important role in many facets of human endeavour

Occurs remarkably frequently in our everyday lives

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


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Statistics in Business

Accounting auditing and cost estimation Economics regional, national, and international

economic 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


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What is Statistics?

Science of gathering, analyzing, interpreting,and presenting data

Branch of mathematics

One page in Courses of study ? Facts and figures Measurement taken on a sample

Type of distribution being used to analyze dataStatistics is the scientific method that enables us to make decisions as responsibly as possible .


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Statistics

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

Collect data Analyze and summarize data Draw conclusions to answer research

questions Statistical Inference

In the presence of variation


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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?


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Decision making process..

1. Collecting pertinent information that is as reliable aspossible.

2. Selecting the parts of the available information that are

most helpful to make rational decisions.3. Making the actual decisions as sensibly as possible on

the basis of the available evidence.

4. Perceiving the risks entailed in the particular decisionmade, and evaluating the corresponding risks of alternative actions.


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Example

Polio Vaccine Results of the Experiment

Vaccine Group 57

Non-vaccineGroup 142


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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 iseasier to lie without them.

--Frederick Mosteller

Figures wont lie but liars will figure.

--Charles Grosvenor


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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 iseasier to lie without them.

--Frederick Mosteller

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


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Population Versus Sample Population the whole

a collection of persons, objects, or items under study The entire group of individuals in a statistical study we

want 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 collectinformation, used to draw conclusions about thewhole (statistical inference


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Statistics can be split into twobroad categories

1. Descriptive statistics

2. Statistical inference


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Descriptive vs. Inferential Statistics

Descriptive Statistics using datagathered on a group to describe or reachconclusions about that same group only

Inferential Statistics using sample datato reach conclusions about the populationfrom which the sample was taken


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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 a

concise description of complex information

(e.g. an average figure) Exhibition of patterns that may be found in

sets of information


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Inferential Statistics..

Especially relates to: Determining whether characteristics of a

situation 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


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Statistics: Science of variability..?

Virtually everything varies Variation occurs among individuals Variation occurs within any one individual

as time passes


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Parameter vs. Statistic

Parameter descriptive measure of thepopulation Usually represented by Greek letters

Statistic descriptive measure of asample Usually represented by Roman letters


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Symbols for Sample Statistics

x denotes sample mea

2S denotes sample varianceS denotes sample standard deviatio


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Process of Inferential Statistics

Population

(parameter )

Samplex

(statistic)

Calculate x

to estimate

Select a

random sampl


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Levels of Data Measurement

Nominal Lowest level of measurement

Ordinal Interval Ratio Highest level of measurement


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Nominal Level Data Numbers are used to classify or categorize

Example: Employment Classification 1 for Educator

2 for Construction Worker 3 for Manufacturing Worker

Example: Ethnicity

1 for African-American 2 for Anglo-American 3 for Hispanic-American


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Example of OrdinalMeasurement

f i

n

is

h

1

2

3

4

5

6


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Ordinal DataFaculty should receive preferential treatment for parking space in new Bharati Telecom building .

1 2 3 4 5

StronglyAgree

Agree StronglyDisagree

DisagreeNeutral


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Interval Level Data

Distances between consecutive integersare equal Relative magnitude of numbers is meaningful Differences between numbers are comparable Location of origin, zero, is arbitrary Vertical intercept of unit of measure transform

function is not zero

Example: Fahrenheit TemperatureExample: Calendar TimeExample: Monetary Utility


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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 transform function

is zeroExamples: Height, Weight, and VolumeExample: Monetary Variables, such as Profit and Loss, Revenues,

and ExpensesExample: Financial ratios, such as P/E Ratio, Inventory Turnover


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Usage Potential of Various

Levels of Data

Nominal

Ordinal Interval Ratio

l


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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, Multiplication, andDivision

All of the above

StatisticalMethods

Nonparametric

Nonparametric

Parametric

Parametric


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Visual presentation of data


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Data preparation rules

Data presented must be factual relevant

Before presentation always check: the source of the data

that the data has been accuratelytranscribed the figures are relevant to the problem


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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


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Graphs

0

10

20

30

40

50

6070

80

90

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

East

West

North


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Pie chart

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr


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Multiple bar chart

0 20 40 60 80 100

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

North

West

East


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Simple pictogram

0

20

40

60

80100

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

East

North

West


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Frequency distributions

Frequency tables

Class Interval Frequency Cumulative Frequency< 20 13 13


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Frequency

0

5

10

15

20

25

30

< 20


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Ungrouped VersusGrouped Data

Ungrouped data have not been summarized in any way are also called raw data

Grouped data have been organized into a frequency

distribution

E l f U d


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Example of UngroupedData

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

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54

Ages of a Sample of

Managers fromXYZ

Freq enc Distrib tion of


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Frequency Distribution of Ages

Class Interval Frequency20-under 30 6

30-under 40 1840-under 50 1150-under 60 11

60-under 70 370-under 80 1


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Data Range

42

30

53

50

52

30

55

4961

74

26

58

40

40

28

36

30

3331

37

32

37

30

32

23

32

58

4330

29

34

50

47

31

35

26

64

4640

43

57

30

49

40

25

50

52

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Smallest

Largest

Range = Largest - Smallest

= 74 - 23

= 51

Number of Classes and Class


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Number of Classes and ClassWidth

The number of classes should be between 5and 15. Fewer than 5 classes cause excessive

summarization.

More than 15 classes leave too muchdetail. 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=651

=WidthClasseApproximat


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Class Midpoint

Class Midpoint =beginning class endpoint + ending class endpoint

2

= 30 + 402

= 35

Class Midpoint = class beginning point +1

2class width

= 30 +12

10

= 35


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Relative FrequencyRelative

Class Interval Frequency Frequency20-under 30 6 .1230-under 40 18 .36

40-under 50 11 .2250-under 60 11 .2260-under 70 3 .06

70-under 80 1 .02Total 50 1.00

650

1850


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Cumulative Frequency

CumulativeClass Interval Frequency Frequency20-under 30 6 6

30-under 40 18 2440-under 50 11 3550-under 60 11 4660-under 70 3 49

70-under 80 1 50Total 50

18 + 611 + 24

Class Midpoints Relative


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Class Midpoints, RelativeFrequencies, and Cumulative

FrequenciesRelative

Cumulative

Class IntervalFrequency Midpoint Frequency Frequency20-under 30 6 25 .12 630-under 40 18 35 .36 2440-under 50 11 45 .22 3550-under 60 11 55 .22 4660-under 70 3 65 .06 4970-under 80 1 75 .02 50

Total 50 1.00

Cumulative Relative


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Cumulative RelativeFrequencies

CumulativeRelative Cumulative Relative

Class IntervalFrequency Frequency Frequency Frequency20-under 30 6 .12 6 .1230-under 40 18 .36 24 .4840-under 50 11 .22 35 .70

50-under 60 11 .22 46 .9260-under 70 3 .06 49 .9870-under 80 1 .02 50 1.00

Total 50 1.00


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Histogram


30-under 40 1840-under 50 1150-under 60 1160-under 70 3

70-under 80 1 0

1 0

2 0

0 10 20 30 40 50 60 70 80

Years

F r e q u e n c y


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Histogram Construction



70-under 80 1 0

1 0

2 0

0 10 20 30 40 50 60 70 80

Years

F r e q u e n c y


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Frequency Polygon



70-under 80 1 0

1 0

2 0

0 10 20 30 40 50 60 70 80

Years

F r e q u e n c y


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Ogive

CumulativeClass Interval Frequency20-under 30 630-under 40 2440-under 50 3550-under 60 46

60-under 70 4970-under 80 50

0

2 0

4 0

6 0

0 10 20 30 40 50 60 70 80

Years

F r e q u

e n c y


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Relative Frequency Ogive

CumulativeRelative

Class Interval Frequency

20-under 30 .1230-under 40 .4840-under 50 .7050-under 60 .9260-under 70 .9870-under 80 1.00

0.000.10

0.200.300.400.500.600.700.80

0.901.00

0 10 20 30 40 50 60 70 80

Years

C u m u

l a t i v

e R e l a t i v

e F r e q u

e n c y


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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 1.00 360.0


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Complaints by Passengers

Stations, Etc.

40%TrainPerformance

21%

Equipment15%

Personnel14%

Schedules,Etc.10%


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SecondQuarter Truck

Production

2d QuarterTruck

ProductionCompany

A

B

C

D

E

Totals

357,411

354,936

160,997

34,099

12,747

920,190

Second Quarter


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39%39%

17%4%

1%

A B C D E

Second Quarter Truck Production

Pie Chart Calculations for


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Pie Chart Calculations for Company A

2d QuarterTruck

Production 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

357,411920,190

=

.388 360 =


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Pareto Chart

0

10

20

30

40

50

60

70

80

90

100

PoorWiring

Short inCoil

DefectivePlug

Other

F r e q u e n c y

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%


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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

G a s o

l i n e

S a

l e s

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