Introduction to STATISTICS-

8/2/2019 Introduction to STATISTICS-

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Introduction toSTATISTICS


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Statisticsis the science of conducting studiesto collect, organize, summarize, analyze,

present, interpret and draw conclusions fromdata.


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What is data?

It is the collection of facts, concepts orinstructions in a formalized mannersuitable for communication or

processing by human. Collection of data is known as a dataset and a single observation a datapoint.


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Statistics- IntroductionMost people become familiar with probability and statistics through

radio, television, newspapers, and magazines. For example, thefollowing statements were found in newspapers.

Based on the 2000 census, 40.5 million households have two vehicles. The average age of top 50 powerful persons in India is decreased from 58 years in

2003 to 54 years in 2006. The average cost of a wedding is nearly Rs 10,00,000.

Women who eat fish once a week are 29% less likely to develop heart disease.


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PopulationThe complete collection of

measurements outcomes, object orindividual under study

SampleA subset of a population, containing

the objects or outcomes that areactually observed

ParameterA number that describes apopulation characteristics

StatisticA number that describes a sample

characteristics

Basic ConceptsData

An information coming fromobservations, counts,measurements, or responses.

The basic idea behind all statistical methods of data analysis is to makeinferences about a population by studying small sample chosen from it


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Samples and Populations


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Descriptive Statistics

Consists of the collection, organization,classification, summarization, andpresentation of data obtain from thesample.

Used to describe the characteristics ofthe sample

Used to determine whether the samplerepresent the target population bycomparing sample statistic and

population parameter


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Inferential Statistics

Consists of generalizing from samplesto populations, performing estimationshypothesis testing, determiningrelationships among variables, and

making predictions. Used when we want to draw a

conclusion for the data obtain from thesample

Used to describe, infer, estimate,

approximate the characteristics of the


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Inferences

Consider:o Average length of females and males:

90cm and 100cm respectively.o Descriptive statistics: the values.o Inference: males are (in general) larger

than females.


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An overview of descriptive statisticsand statistical inference

StatisticalInference

DescriptiveStatistics

No

Yes


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Data Collection

Collect datao e.g. Survey

Present datao

e.g. Tables and graphs

Characterize datao e.g. Sample mean =

Mean weight is 120 pounds


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Types of data

Qualitative/ Categorical andQuantitative/Numericalo Nominal, Ordinal, Interval and Ratioo Discrete

--Nominal and ordinalo Continuous

-- Interval and ratio Cross-sectional , Temporal and Spatial


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Data Types

Data

Qualitative QuantitativeData Types

Nominal Ordinal Interval RatioLevels of

Measurement

Discrete Discrete or continuous


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Qualitative/ Categoricalvariables Here, data are classified on the basis

of some attribute or quality such asgender, literacy, religion, employment

etc. These attributes under study cannotbe measured.

One can only find out whether it ispresent or absent in the units ofpopulation under study.


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Example

Attribute under studyblindness Here, we can determine how many

persons are blind in a given population. It is not possible to measure the degree

of blindness in each case. Attributes can be: Gender (Males and females) Literacy (literates and illiterates)

Employment (employed and

unemployed)


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Two types of categorical variables

Nominal Ordinal


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Nominal data

Nominal data are the labels orassigned numbers.

Car number

Roll number STD code Color of bike House number Such data are used for identifying

individuals and places .


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Ordinal data

Ordinal data can be arranged inorder such as worst to best or bestto worst

Same as nominal but there is an orderwithin the groups into which the datais classified.

Unable to say by how much they differ

from each other.-- Rating of hotels, restaurants andmovies.


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Quantitative/Numericalvariables Here, the data are classified on the

basis of some characteristics capableof quantitative measurements such

as:

Marks scored by students in class Height of individuals Income of individuals

Age of individuals Expenditure of individuals


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Two types of Quantitativevariables

Interval data Ratio data Quantitative variables can be discreteor continuous.


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Interval data

Interval data can be on a numericalscale .

zero point does not mean absence

of property.

Temperature


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Ratio data

It possess all the properties of intervaldata with meaningful ratio of twovalues

Ratio data differ from interval data inthat there is a definite zeropoint(nothing exists for the variable atzero point)

Height Weight Price Length Sales revenue


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Discrete variables

The variables is said to be discrete if itassumes only some specific values.

Discrete variables arises in a

situation where counting isinvolved.o number of credit cards held by an

individual

o number of defective items in boxes of 100items

o number of students in the class


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Continuous variables

Continuous variables arises insituations when some sort ofmeasurement is involved in range.o life of an electric bulbo waiting time for customers at a banks

counter.o rainfallo

temperature

Case Let


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The ABC Marketing Corporation has asked you for informationabout the car you drive. For each question, identify each of the typesof data requested as either Qualitative data or Quantitative data.When numeric data is requested, identify the variable as discrete orcontinuous.1. What is the weight of your car?2. In which city was your car made?3. How many people can be seated in your car?4. Whats the distance traveled from your home to your school?5. Whats the color of your car?6. How many cars are in your household?7. Whats the length of your car?

Case Let


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Levels of Measurement

Level Put incategories

Arrangein order

Subtractvalues

Dividevalues

Nominal Yes No No No

Ordinal Yes Yes No No

Interval Yes Yes Yes No

Ratio Yes Yes Yes Yes


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Cross-sectional Data

Cross-sectional data comprises of a variable recordedover at the same point or period of time for manyindividuals , organization, places etc.o

Ages of all students at the time of joining IMS , in theyear 2008.o Number of students enrolled in IIM, in the year 2008.o Stock prices of Infosys Technologies, TCS, and

Wipro on31st March 2008.o Population of Delhi, Mumbai , Chennai and Kolkata

as per 2001 census.


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Temporal Data

Temporal data also referred as time-seriesdata , is the data about an individualorganization , places etc over a period of time.

Marks obtained by student from standardI to XII.

Total business of ICICI bank as at the endof last five years.

Population of India from the year 1931 to2001


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Spatial Data

Spatial data is the data based ongeographical location basis.

Income tax collection from variousstates

Sales of Times Of India in Delhi.Production of wheat in different states

of the country


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Data Collection Techniques

Method of DataCollection

Data collected andrecorded by

others(secondarystudy)

Data collected directlyfrom the field of

enquiry(primary data)


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Primary Data

Data originally collected in the process ofinvestigations are known as primary data.

Primary data consists of figures collectedat first hand in order to satisfy the

purpose of a particular statistical enquiry. Merits :

o Original in natureo More reliable and accurateo Can be used with greater confidence bz the

enquirer knows its origin.o Exactly matches the needs of the project.


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Demerits :o Expensiveo Time-consumingo Collection of data involves creating new

definitions and measuring instrumentssuch as questionnaires or interview formsand training people to use thesespecifically designed instruments.


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Collection ofPrimary Data

Mailed QuestionnaireMethod

Direct PersonalInvestigation

Indirect OralObservation

ObservationInterviewSchedule Sent Through

Investigator


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Collection of primary data

Direct personal investigationo Personal interview ( the investigator personally

approaches each informant and gathers therequired information)

o Personal observation ( here, rather than askinganybody, the investigator personally observesand records the information related to aparticular field)

Indirect oral observation (here, instead of

directly approaching the actual field or person,data are collected from third party informant)

Questionnaire method ( here, a well-prepared questionnaire is given to a list of

persons with the request to return them duly


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Designing a Questionnaire

The no. of questions should be as few aspossible

Questions should be of objective type.Yes or no type or simple tick marking

answers are preferred. Questions should be properly arranged to

have a systematic and easy flow ofanswer.

Questions affecting the sentiment andpride of the respondent should beavoided.

Necessary instructions and guidelines


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Types of Questionnaires

Structured or Non structuredquestionnaire.

Disguised and Non disguised

questionnaire.

Structured or Non structured


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Structured or Non structuredquestionnaire

Structured questionnaire: consists of a set ofquestions arranged in a predetermined order .Each question requires the respondent to make

a choice among a few given predeterminedresponses.

Example : How frequently do you go to watch a movie? Choices (Very frequently, often, sometimes,

never) Such questions are called closed questions.


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Non Structured questionnaire: consists ofwhat are called open-ended questions.

Example: How do you spend your free time? How do you describe the ambience of the

new store? Such questions give the respondent

freedom to answer according to their viewsand opinions.

Disguised and Non disguised


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Disguised and Non disguisedquestionnaire

Non

disguised questionnaire: here, thepurpose or objectives of the study are madeknown to the respondent.

Disguised questionnaire: here, respondents arenot taken into confidence regarding purpose orobjectives of the study.

Disguised questionnaire is not very popular asrespondents may not be forthcoming in theiranswers when they do not know the objectivesor relevance of the questions or the study.

S d d


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Secondary data

Secondary data consists of figureswhich were collected originally tosatisfy a particular enquiry but noware being used for different enquiry.

Sources of secondary data:o Journalso Reportso Government and non-Governmentpublications.

C


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Collection ofSecondary Data

Journals,

News-papers

Publication by

Government /InternationalOrganization

Universities

and ResearchOrganizations

BooksInternet


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Merits :o Readily availableo Less expensive compared to primary datao Less time consuming compared to primary

data

Demerits :o These may not be relevant in the present

context.o

These may not have the needed accuracy orreliability.o These may not be adequate.

T pes of secondar data


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Types of secondary data

Internal or external Internal

o Company Reports , Intranet External

o Newspaper, magazines, websites, RBIpublications

Summary


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The two major areas of statistics are descriptiveand inferential. When the populationsto be studied are large, statisticians usesubgroups called samples. Data can be classified as qualitativeor quantitative. The four basic types of measurement are nominal, ordinal,

interval, and ratio.

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