Stat Basic=Chapter01

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Copyright 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 1Introduction


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What is Statistics?


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Definition of Statistics

Reasons of Studying Statistics

Types of Statistics

Types of VariablesLevel of Measurement

Uses and Abuses of Statistics.


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The word statisticsis

used to refer to Numerical information

Such as the---- average starting salary of

University Graduates,

Average number ofstudents appeared in SSC

examination

What

is

Meant

by

Statistics?


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Statisticsis the science of

collecting, organising,presenting, analysing and

interpreting data to assist

in making more effectivedecisions.

What

is

Meant

by

Statistics?


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it is the artand scienceof

collecting

organizing

presenting data

drawing inferencesfrom asample ofinformationabout an entire population

as well as

predicting and

developing policy analysis

What

is

Meant

by

Statistics?


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WhousesStatistics?

Those using Statistical techniques include :

Marketers

Accountants

Hospitals

Investors

EconomistsSports people

StatisticiansConsumers

Educators

Quality Controllers

Politicians Physicians


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Data are everywhere

Statistical techniques are used to make

many decision that affect our lives

No matter what your future line of

work, you will make decisions that

involve data.


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Types of

Statistics


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Types of Statistics

Methods ofcollecting

organizing

presentingand

analyzingdata

Science ofmakinginferences

abouta population,

based onsampleinformation.

Descriptive Inferential


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Descriptive Statistics

are methodsof organizing, summarizing,

and presenting data in a convenient and

informative way.

EXAMPLE 1: According to Consumer Reports,General Electric washing machine owners reported9 problems per 100 machines during 2001. Thestatistic 9 describes the number of problems out ofevery 100 machines.

These methods include:

Tabular, Graphical Techniques

Numerical Techniques


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Descriptive Statistics

The actual method used depends on what in format ionwe would like to extract. Are we interested in

measure(s) of central location? and/or

measure(s) of variability (dispersion)?

Descriptive Statistics helps to answer these

questions


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Inferential Statistics

Descriptive Statistics describe the data set

thats being analyzed, but doesnt allow us todraw any conclusions or make any

interferences about the data. Hence we need

another branch of statistics: inferent ial

stat ist ics.

Inferential statistics is also a set of methods,

but it is used to draw conclusions orinferences about characteristics of

populat ionsbased on data from a sample.


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Statistical Inference

Statistical inference is the processof making an

estimate, prediction, or decision about apopulation based on a sample.

Parameter

Population

Sample

Statistic

Inference

What can we inferabout a Populations Parameters

based on a Samples Statistics?


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Statistical Inference

We use statistics to make inferences

about parameters.

Therefore, we can make an estimate,

prediction, or decision about apopulation based on sample data.

Thus, we can apply what we know about

a sample to the larger population from

which it was drawn!


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Statistical Inference Rationale:

Large populations make investigating eachmember impractical and expensive.

Easier and cheaper to take a sample and make

estimates about the population from the sample.

However:

Such conclusions and estimates are not always

going to be correct.

For this reason, we build into the statisticalinference measures of reliability,namely

confidence level and significance level.


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Confidence & Significance Levels

The conf idence levelis the proportion of times

that an estimating procedure will be correct.E.g. a confidence level of 95% means that,

estimates based on this form of statistical

inference will be correct 95% of the time.

When the purpose of the statistical inference is to

draw a conclusion about a population, the

signi f icance levelmeasures how frequently the

conclusion will be wrong in the long run.

E.g. a 5% significance level means that, in the

long run, this type of conclusion will be wrong

5% of the time.


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Identify the following

C. Coca-cola tasters sip a few drops

of coke to make a decision

with respect to all the coke

waiting to be released for sale.

A. A Gallup poll found that 83%

of the people in a survey knew

which country won the gold

medal in Mens Hockey in 2002.

B. The accounting department of

a firm will select a sample of

invoices to check for accuracy of

all the invoices of the company.

Descriptive Inferential


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19

Types of Statistics / Branches of Statistics

Statistics

Descriptive Statistics Inferential Statistics

Non-Parametric StatisticsParametric Statistics


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Population

A collection of all possible individuals, objects ormeasurements of interest.

Sample

A portion, or part, of the population of interest.

Observation

An observation is the value, at a particular period, of a

particular variable. Variable

A symbol that stands for a value that may vary.

in (computer programming), a symbolic name associated

with a value and whose associated value may be changed. Data

Data are the observed valuesof a variable.

E.g. student marks: {67, 74, 71, 83, 93, 55, 48}


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A population is acollection of

all possibleindividuals,objects,

ormeasurements of interest


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Take a

What we now need is

From

which are deemed to be representative of the


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Take aMeasurement

for each one

in the sampleRecord


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Why take a sample instead of studying

every member of the population?

Costs of surveying the entire population

may be too large or prohibitive

Destruction of elements during

investigationAccuracy of results


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Types of Variables

a characteristic

of

a population orsample

that is of interest to us

A Variable


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QuantitativeQualitative

Numerical

Observations

Categorical

Observations

Variables

Types of Variables


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Country of Birth

U.K.Germany

Taiwan

China

IndiaJapan

Russia

Eye Colour

Blue

Brown

HazelGreen

Red

Gender

Male

Female

Qualitativeor Attr ibute

Variables


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Minutes to end

of Class55

45

30

5

0

Number of

Children in

a Family

1234

Number of

Two-DoorGarages

in a Street

10203040...

Number of

Satisfied

Facebook Fans

0203040

QuantitativeNumeric

Variables


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Quantitative

Numerical

Observations

can be classified as eitherDiscrete or

Continuous

Discrete can only assumecertain valuesand

there are usually gapsbetween values

e.g. - Number of bedroomsin a house

- Number of Students in AUST

Variables

Characteristics


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Continuous can assumeanyvaluewithina specified range!

e.g. - Pressurein a tire

- Weight of a shipment

- Height of studentsin a class

QuantitativeNumerical

Observations

can be classified as eitherDiscrete or

Continuous

Characteristics

Variables


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Summary of Types of Variables

Variable

Qualitative

Categorical

Observations

QuantitativeNumerical

Observations

Discrete Continuous

(number of children) (time used for an exam)


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Types of variables


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Nominal/Categorical

Ordinal/Rank

Interval

Ratio


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Nominal

Data can only be classif ied into categoriesor counted

and cannotbe arranged in any particular order

Example Pran

Classification:

Category: CandyBy Colour only(No natural order)


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Nominal

Example Pran

Data categories are mutually exclusive: anindividual, object, or measurement is included inONLY ONECATEGORY

Data categories are exhaustive: Each individual, object, or

measurement MUST APPEARin one of the categories

Data categories have no logical order.


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Ordinal

involves data arranged in some order,but

the differencesbetween data values

cannot be determined or are meaningless!

Example During a taste test of 4 mineral water:

Mum was ranked number.... 1.

Pani number. 2.

Fresh number....... 3.

Spa number ...4.


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Ordinal

involves data arranged in some order,but

the differencesbetween data values

cannot be determined or are meaningless!

Example You are asked to rate the instructor of the course BBA 122

Rating Frequency

Superior-----------------------------------6Good--------------------------------------26

Average------------------------------------8

Poor----------------------------------------7

Inferior------------------------------------3


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Ordinal

We can only conclude that a rating of good is betterthan a rating of poor.

We can not conclude how much better than the rating is.

Data categories are mutually exclusive and

exhaustive Data categories are ranked or ordered according to

the particular trait they possess.


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Interval

similar to the Ordinal Level,

with the additional property

that meaningful amounts of differences between data

values can be determined.

There is no natural zero point

Example

Temperature on theCelsius scale.


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Interval

Data categories are mutual ly exclusive and exhaustive

Data categories are scaledaccording to the amount of thecharacteristics they possess.

Equal differences in the characteristics are represented by

equal differences in the numbers assigned to the categories


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Ratio

the Interval Levelwithan inherent zerostarting point.

Differences and ratios are meaningfulfor this level of measurement.

Examples

Monthly income of surgeons

Distance travelled by manufacturersrepresentatives per month


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Ratio

Data categories are mutual ly exclusive and exhaustive

Data categories are scaledaccording to the amount of thecharacteristics they possess.

Equal differences in the characteristics are represented by

equal differences in the numbers assigned to the categories.

The point 0 reflects the absence of the characteristic.


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Summary of the Characteristics for Levels of

Measurement

45


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46

Limitations of statistics

1. Statistics is not suitable to the study of qualitative phenomenon

2. Statistics does not study individuals

3. Statistical laws are not exact

4. Statistics table may be misused

5. Statistics is only, one of the methods of studying a problem


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Benjamin Disraeli said

There are three kinds of lies
http://c/Documents%20and%20Settings/Colleen/Local%20Settings/Temp/Stats_2_ProbSample_B.ppt


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Figures dont lie.

L iars f igure!

Caution

C ti


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As you begin to study statistical methods,

you are cautionedto take what you see published as

statistical facts

with a healthy grain of skepticism!

an average may not be representativeof all the data

graphs can also be misleading

be sure to study the sampling methods

For Example

Caution

1 1C ti


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Caution

Review the following three slides and

notice the effect

that thedifferent scales

have on your interpretation of the

pattern betweenCrimeand Unemployment Rates.

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1986 - 1999

0 1 2 3 4 5 6 7 8 9 10 11 12

3200

30002800

2600

2400

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2000

Chart A

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1986 -1999

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3000

25002000

1500

1000

500

0

Chart B

500

0

1000

1500

20002500

3000

1 54


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1986 -1999Chart C

3200

30002800

2600

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7 8 9 10 11 12

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1986 -1999

Chart CChart A Chart B

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This completes Chapter 1.