Intrdn. Statistics

7/28/2019 Intrdn. Statistics

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I ntroduction

to Statistics


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A decision of opening up retailsector for FDI cant be taken in a

hurry


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Retailing Sector

Total retail business in India is over Rs 12, 00,000crore, a third of our GDP

After agriculture, it is the largest employer withover 22 million people engaged in it

Throw out the self-employed51 per cent of ourtotal workforce

Unorganized Sector98%

Unorganized sector makes up for 92% of ourentire workforce

Between 2005 and 2010, against the official claimof creating more than 50 million jobs, actuallyonly two million jobs were created


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Retailing Sector

Industry would need additional manpowerof 15 to 30 million in 10 years, if reformsdo happen

The industry currently employs 35 millionpeople

Requirement of an estimated 25 to 30million additional people by 2020

In about 10 years, we would provide directand indirect employment opportunities toapproximately 20,000 people in the storesitself


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What is Statistics?

Science of gathering, analyzing,interpreting, and presenting data

Branch of mathematics

Course of study Facts and figures

A death

Measurement taken on a sample Type of distribution being used to analyze

data


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Population Versus Sample

Populationthe whole- a collection ofpersons, objects, or items of interest

A defined categoryA group of people

A set of objects

Censusgathering data from the entirepopulation

Samplea portion of the wholea subset of the population


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Population


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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 15GY2 Gray 18

GY3 Gray 17


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Sample and Sample Data

Identifier Color MPG

RD2 Red 10

RD5 Red 13

GR1 Green 35

GY2 Gray 18


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Descriptive vs. Inferential Statistics

Descriptive Statisticsusing data gatheredon a group to describe or reach conclusions

about that same group only

Inferential Statisticsusing sample data toreach conclusions about the population from

which the sample was taken


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Descriptive Statistics Inferential Statistics

Collect

Organize

Summarize

Display

Analyze

Predict and forecast values

of population parametersTest hypotheses aboutvalues of population

parameters

Make decisions


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Descriptive statistics in manufacturing

batteries to make better decisions

total number of worker hours per plant perweek - help management understand laborcosts, work allocation, productivity, etc.

company sales volume of batteries in a year- help management decide if the product isprofitable, how much to advertise in comingyear, compare to costs to determine

profitability. total amount of sulfuric acid purchased per

month for use in battery production. - canbe used by management to study wasted

inventory, scrap, etc.


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Inferential Statistics in manufacturing

batteries to make decisions take a sample of batteries and test them to

determine the average shelf life - use the sampleaverage to reach conclusions about all batteries ofthis type. Management can then make labelingand advertising claims. They can compare thesefigures to the shelf- life of competing batteries.

Take a sample of battery consumers and determinehow many batteries they purchase per year. Inferto the entire population - management can use thisinformation to estimate market potential and

penetration

Interview a random sample of production workersto determine attitude towards companymanagement - management can use this surveyresults to ascertain employee morale and to directefforts towards creating a more positive working

environment which, hopefully, results in greaterproductivity.


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Descriptive statistics in recorded music

industry

total sales of compact discs this week,number of artists under contract to acompany at a given time.

total dollars spent on advertising last monthto promote an album.

number of units produced in a day.

number of retail outlets selling the

company's products.


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Inferential statistics in recorded music

industry

measure the amount spent per month onrecorded music for a few consumers thenuse that figure to infer the amount for thepopulation.

determination of market share for rap musicby randomly selecting a sample of 500purchasers of recorded music.

Determination of top ten single records by

sampling the number of requests at a fewradio stations. Estimation of the average length of a single

recording by taking a sample of records and

measuring them.


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Parameter vs. Statistic

Parameterdescriptive measure of thepopulation

Usually represented by Greek letters

Statisticdescriptive measure of a sampleUsually represented by Roman letters


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Symbols for Population Parameters

denotes population paramet

2

denotes population variance

denotes population standard deviatio


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Symbols for Sample Statistics

x denotes sample mea

2S denotes sample variance

Sdenotes sample standard deviatio


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Process of Inferential Statistics

Population

(parameter )

Sample

x

(statistic)

Calculate x

to estimate

Select a

random sampl


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Variables

Categorical DataQualitative or Nominal Variables

Numerical Data

Discrete or Continuous Variables


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Example 1

Name of Internet provider

Amount of time spent surfing Internet

No. of online purchases made in a month

No. of emails received in a week


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Example 2

Number of telephones per household

Length (in minutes) of longest long-distancecall made per month

Whether there is a telephone line connectedto a computer modem

Whether there is a fax machine in thehousehold


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Example 3

Amount of time spent shopping in thebookstore

Number of textbooks purchased

Academic qualification Gender


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Levels of Data Measurement

NominalLowest level of measurement

Ordinal

ScaleInterval

RatioHighest level of measurement


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Nominal Level Data

Numbers are used to classify or categorizeExample: 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

More Examples: Gender

Religion Geographical location Place of Birth Telephone numbers Employee ID numbers


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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 of employees

Example: Taste test ranking of three brands of soft drinkExample: Position within an organization

1 for President2 for Vice President3 for Plant Manager

4 for Department Supervisor5 for EmployeeMore Examples:

Computer TutorialMutual Funds

Top Companies


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Example of Ordinal Measurement

fi

n

i

s

h

1

2

3

4

5

6


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Ordinal Data

Faculty and staff should receive preferential

treatment for parking space.

1 2 3 4 5

StronglyAgree

Agree StronglyDisagree

DisagreeNeutral


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Interval Level Data

Distances between consecutive 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 transform

function is not zeroExample: Fahrenheit TemperatureMore Examples:

Percentage Change in employmentPercentage Return on a stock

Dollar Change in Stock Pricey = b + ax


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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)

Examples: Height, Weight, and VolumeExample: Monetary Variables, such as Profit andLoss, Revenues, and Expenses

Example: Financial ratios, such as P/E Ratio,Inventory Turnover, and Quick Ratio.

More Examples: Number of trucks sold, Complaints

per 1,000 customers, Number of employeesy = ax


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Usage Potential of Various

Levels of Data

Nominal

Ordinal

Interval

Ratio


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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, and

Division

All of the above

StatisticalMethods

Nonparametric

Nonparametric

Parametric

Parametric

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Intrdn. Statistics