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Introduction To

Statistics

What is Statistics ?

Statistics has become an important subject

having useful applications in various walks of life.

Statistical is a discipline which is concerned with:

1.Designing experiments and collection of data.

2.Summarizing information to aid understanding.

3.Drawing conclusions from data

4.Estimating the present and predicating the

future.

What is Statistics ?

The word Statistics is derived from the

Italian word “StatistaStatista” or Latin word “StatusStatus” ”

both meaning Political State.

The purpose of Statistics is to develop and

apply methodology for extracting useful

knowledge from data.

Meaning of Statistics ?

Statistics is described in two senses:

Plural noun: describes a collection of numerical

data.

Singular noun: describes as a branch of applied

mathematical science pertaining to the collection,

analysis, interpretation or explanation and

presentation of data. It also provides tools for

prediction and forecasting based on data.

Meaning of Statistics ?

“Statistics is a way to get information from data”.

Meaning of Statistics ?Meaning of Statistics ?

“Statistics is a way to get information from data”.

Data:Data: Facts, especially numerical facts, collected together for reference or information.

Statistics:Statistics: is a tool for creating new understanding from a set of numbers.

Information:Information: Knowledge communication concerning some particular facts.

Definition of Statistics ?

“Statistics refers to the body of techniques

which has been developed for the collection,

presentation and analysis of quantitative data

and for the use of such data in decision”.

-Nester &

Wasserman.

“Statistics is a body of methods of making wise wise

decisionsdecisions in the face of uncertainty”.

–W.A Wallis & H.V.

Robert.

“Major activities in Statistics involves:

•Collection of Data

•Organization of Data

•Presentation of data

•Analysis of data

•Interpretation of data.

Definition of Statistics ?

Branches of StatisticsBranches of Statistics

Descriptive Statistics:

is concerned with exploring,

visualizing and summarizing data but without

fitting the data to any models.

Such as- Frequency count, ranges

Means, Mode, Median, Variance & Standard

Deviation.


Inferential Statistics:

are used to draw inferences about

a population from a sample.

There are two methods:1. Estimation

2. Hypothesis

testing.

Estimation:Estimation: Estimate the population mean weight

using the sample mean weight.

Hypothesis testing: Hypothesis testing: Test the claim that the

population mean weight is 74 K.g.


Business Managers & Business Statistics

A very basic role business manager

has to perform is to take business decisions.

Business decision making is a

process of selecting the best out of alternative

opportunities open to firm.

Many business decisions are taken

under the condition of uncertainty & risk.

Use of statistics helps to identify

the uncertainty & reduce risk up to the

extent.

What is Business Statistics?What is Business Statistics?

Business Statistics:

Business Statistics is application of

Statistical tools and techniques in business

Decision making.

Business Statistics is a

science assisting you to make business

decisions under uncertainties, based on some

numerical and measurable scales.

Decision making processes

must be based on data, neither on personal

opinion nor on belief.

What is Business Statistics?What is Business Statistics?

1. Statistics does not deal with individual

measurement

2. Statistics cannot be used to study qualitative

phenomenon

3. Statistical results are true only on an average.

4. Statistical data being approximations, are

mathematically incorrect.

5. Statistical laws are not exact.

6. Statistical table may be misused

7. Statistics is only one of the methods of studying a

problem

Limitations of StatisticsLimitations of Statistics

BasicStatistical Concepts

1. Population

2. Census

3. Sampling & Sampling Principles.

4. Parameter

5. Statistic

Basic Statistical ConceptsBasic Statistical Concepts

The group of individuals or units under

study is called as Population or Universe.

The population may be finite or infinite.

Finite PopulationFinite Population: : consists of finite number of units.

For ex. No. of workers in the factory

Infinite Population: Infinite Population: if it has infinite number of units.

For ex. No. of people seeing television programme.

Population

Information on population can be collected in two

ways:

1. Census method

2. Sample method

Census Method: In census method each any every

element of the population is included in the

investigation.

Sample method: Few representative items of the

universe under study is called as sample.

Census/Sampling Census/Sampling

Merits of Census:

1. Data will be collected from each and every item of population.

2. Accurate and reliable results.

3. Intensive study is possible.

4. Information may be used for further survey.

Limitations Census:

1. Costly method.

2. It requires more money, time, labour & energy.

3. It is not possible where the population is infinite.

4. Sometime only sample method can be used.

Census/Sampling Census/Sampling

Sample:

Finite subgroup of population that is representative

items of the universe under study is called as sample.

Sampling:

The process selecting a Sampling from a population is

called sampling. In sampling representative sample of

elements of a population is selected and then

analyzed.

Sampling Sampling

Sample:

The theory of sampling is based on the principle

of statistical regularity.

It state that a moderately large number of items

chosen at random from a large group are almost sure

on an average to possess the characteristics of the

large group.

Principles of Sampling Principles of Sampling

Following are the principles of Sampling:

1.Principle of Statistical Regularity

2.Principle of large number

3. Principle of validity

4. Principle of optimisation


Following are the principles of Sampling:

1.Principle of Statistical Regularity : It state that

a moderately large number of items chosen at random

from a large group are almost sure on an average to

possess the characteristics of the large group.

2.Principle of large number: other things being

stable as the sample size increase the accuracy of

results increase.


3.Principle of validity: It state that sampling

method provides valid estimate about the population

parameter.

4.Principle of Optimization: This principle state

desirability of obtaining optimum sample design.


ParameterParameter is a characteristic of a population.

The statistical constants of population like

mean(µ), variance(σ2), Skewness (ß1 ), kurtosis (ß2 ),

correlation coefficient (p) etc. are called as

parameter.

Generally the population parameters are

unknown.

Parameter/StatisticParameter/Statistic

Parameter is a characteristic of a population

whereas statisticstatistic is a characteristic of a sample.

Certain measures worked out from sample such

as mean, median, mode or variance, standard

deviation are called statistic(s).

Parameters are the function of population values

while statistics are functions of sample observation.

Generally, the population parameter are

unknown and they can be estimated by appropriate

sample statistics.

StatisticStatistic

Parameter/StatisticParameter/Statistic

Inferential statistics helps us to guess about

population parameters based on random

sampling.

Sampling:

• The way of selecting the sample is known as

sample design.

– (i) ) Probability Sampling

– (ii) Non Probability Sampling

29

Types of sample design.Types of sample design.

Types of Sampling

Simple Random Sampling

Stratified Random Sampling

Systematic Sampling

Cluster Sampling

Probability Sampling Non Probability Sampling

Snowball Sample

Quota Sample

Convenience Sample

Multi Stage

Sample

Sequential Sample

Judgmental sampling

(ii)Probability Sampling

• Probability sampling is a method of sampling that

ensures that every unit in the population has a

known non zero chance of being included in the

sample.

31


• It is foundation of probability sampling.

• In probability sampling every unit has equal chance

to be included in a sample.

• Sampling with replacement: when the sampling

is with replacement, the units drawn are placed

before the next selection is made.

• Sampling without replacement: when the

sampling is without replacement, the units drawn

are not placed before the next selection is made.

• Lottery method is mostly used method for sample

section. 32

Simple Random Sampling:Simple Random Sampling:

If the population is heterogeneous then

stratified sampling technique is applied so as to

obtain a representative sample.

Under it population will be divided into

number of groups called strata in such a manner that

the units within a stratum are homogeneous and

the units between the strata are heterogeneous.

Then next step is to select a sample

using simple random sample of appropriate size from

each stratum. 33

Stratified Random Sampling:Stratified Random Sampling:

In systematic sampling units are selected from the

population at a uniform interval.

Say, select every 15th name on a list, select every 10th

house on one side of a street and so on.

To facilitate this one has to arrange items in numerical,

alphabetical or in any other manner.

This method can be used only when the complete list of

population is available.

34

Systematic Sampling:Systematic Sampling:

Cluster sampling involves grouping the population

and then selecting the groups or the clusters groups or the clusters rather

than individual elements for inclusion in the sample.

For Example:

1. Suppose some departmental store wishes to sample its

credit card holders.

2. It has issued its cards to 15,000 customers. The sample

size is to be kept say 450.

3. For cluster sampling this list of 15,000 card holders could

be formed into 100 clusters of 150 card holders each. Three

clusters might then be selected for the sample randomly.

Area sampling: Area sampling: If clusters are formed considering

geographic area it is called as Area sampling.35

Cluster Sampling:Cluster Sampling:

Cluster sampling involves grouping the population

and then selecting the groups or the clusters groups or the clusters rather

than individual elements for inclusion in the sample.

For Example:

1. Suppose some departmental store wishes to sample its

credit card holders.

2. It has issued its cards to 15,000 customers. The sample

size is to be kept say 450.

3. For cluster sampling this list of 15,000 card holders could

be formed into 100 clusters of 150 card holders each. Three

clusters might then be selected for the sample randomly.

Area sampling: Area sampling: If clusters are formed considering

geographic area it is called as Area sampling.36

Cluster Sampling:Cluster Sampling:

Multi-stage sampling:Multi-stage sampling:

This is a further development of the idea of cluster sampling.

Under multi-stage sampling the first

stage may be to select large primary sampling units

such as states, then districts, then towns and finally

certain families within towns.

37

Sequential sampling: Sequential sampling:

• This is somewhat a complex sample design.

• Size of the sample is not fixed in advance but is determined according to mathematical decisions on the basis of information yielded as survey progresses.

• This design is usually adopted in the in the context of statistical quality control.

• In practice, several of the methods of sampling described above may well be used in the same study

38

(ii)Non Probability Sampling

• Also known as purposive or deliberate sampling

• This sampling method involves purposive or

deliberate selection of particular units from the

universe for the study.

• It includes two types of Sampling

– Convenience sampling

– Judgment sampling

– Quota sampling39


Convenience sampling: when population

elements are selected for inclusion in the

sample based on the ease of access, it can be

called convenience sampling .

Judgment sampling: the researcher judgment is

used for selecting items which he considered as

representative of the population.

Quota sampling: In this method interviewers are

simply given quota to be filled from different

strata. The actual selection of items, left to the

interviewer’s judgment.40

Non Probability Sampling Non Probability Sampling

Data Measureme

nt

Measurement & scaling Measurement & scaling techniquestechniques

Measurement:

By measurement we mean the process of assigning numbers to objects or observations.

Properties like weight, height, length etc., can be measured directly with some standard unit of measurement etc.

However it is difficulty to measure properties like motivation to succeed, ability to stand against stress etc.

Researcher has to create various scaling technique so that each and every variable under study can be measure accurately.

42

Nominal ScalesNominal Scales

Ordinal ScalesOrdinal Scales

Interval ScalesInterval Scales

Ratio ScalesRatio Scales

Four Basic Scales of Measurement

Nominal scale:Nominal scale:Nominal scale is simply a system of assigning number symbols to events in order to label them.

For ex. Numbers on the cricket players jersey .

These numbers does not have any ordered scale.

These numbers are not useful to conduct any further statistical calculations..

In spite of all this nominal scales are still very useful for classifying major sub-groups of the population.

44

If one describes respondents in a survey according to their occupation such as banker, doctor, computer programmer one has used a nominal scale.

If one has used question as check all the brands you would consider purchasing

I. Sony

II. Videocon

III. Samsung

IV. L. G45

Nominal scale:Nominal scale:

Ordinal scaleOrdinal scale

The ordinal scale places events in order.

Rank orders represent ordinal scales and are

frequently used in research relating to qualitative

phenomena.

A student’s rank in his graduation class involves

the use of an ordinal scale.

The appropriate measure of central tendency is

the median.46

For example if one has used question such, as please rank each brand in terms of your preference such as “1” represent your first choice, and “2” represent your second choice, and so on.SonyVideoconSamsungL.GB.P.LPhillips

The ordinal scale places events in order.

47

Ordinal scaleOrdinal scale

48

Interval scaleInterval scale

Interval scale Interval scale Interval scale Examples:

If customers were asked to evaluate a salesmen performance from the list, such as:

A.Extremely friendly

B.Very friendly

C.Somewhat friendly

D.Somewhat unfriendly

E.Very unfriendly

F.Extremely unfriendly

49

• (c) Interval scale Examples:

Please rate each brand in terms of its overall

performance.

50

Interval scaleInterval scale

(d)Ratio Scale:(d)Ratio Scale:

Ratio scales are the ones in which true zero origin exists such as actual number of purchases in a certain time period, rupees spent, miles traveled etc.

A ratio scale allows the researcher not only to identify the absolute differences between each scale point but also to make absolute comparisons between the responses.

51

(d)Ratio Scale:(d)Ratio Scale:d) Ration scale Examples:

Please indicate your age in year________

Approximately how many times in the last

month have you purchased anything over Rs. 1000

in value at BigBazar?

0 1 2 3 4 5 (More specify_ _ _ _ )

52

ScaleNominal Numbers

Assigned to Runners

Ordinal Rank Orderof Winners

IntervalPerformance

Rating on a

0 to 10 Scale

Ratio Time to Finish, in

Seconds

Primary Scales of Measurement

7 38

ThirdThirdplaceplace

SecoSecondnd

placplacee

FirstFirstplaceplace

FinishFinish

FinishFinish

8.2 9.1 9.6

15.2 14.114.1 13.4

Frequency Tables, Charts,

& Graphs.

IntroductionIntroductionA basic role Business Manager has to

perform at every step is to take decisions. For it he

has to collect huge amount of data. However the

collected data are in a ungrouped & raw format. In

order to facilitate decision making certain

processes need to be done on the data and those

are:

1. Classification & Tabulation

2. Diagrammatic presentation

3. Graphical presentation55

ClassificationClassificationIs the ways of presenting the raw data in an

orderly and systematic manner which helps for

further analysis and interpretation of data.

Classification id the process of arranging

things in groups according to their similarity, or

identity.

For ex. Students in the class can be arranged

according to their: gender, Basic graduation, rural

& urban, experience & inexperience etc. 56

Types of ClassificationTypes of Classification

1.Chronological Classification

2.Geographical Classification

3.Qualitative Classification

4.Quantitative Classification

57


In ChronologicalChronological Classification the

collected data will be arranged according to the

time of expressed in year, months, weeks etc.

58


In Geographical Geographical Classification the

collected data will be arranged according to

geographical region.

For ex.

59


Quantitative Quantitative Classification refers to the

classification of data according to some

quantitative phenomena, such as height, weight

length etc.

In this type of classification there are two important

elements:

1. The variable

2. The Frequency. 60

Frequency DistributionFrequency DistributionThe frequencyThe frequency of an observation is the

number of times that observation occurs

Frequency Frequency distribution is a series when a number of observations with similar of closely related values are put in separate bunches or groups.

Three main reasons for preparing frequency distribution:

1. To estimate frequency of population from the sample data.

2. To facilitate the computation of various statistical data.

3. To facilitate the analysis of data.61

Frequency DistributionFrequency DistributionIn a survey of 40 families in a village, the

number of children per family was recorded and the following data obtained.

1, 0, 3, 2, 1, 5, 6, 2, 2, 1, 0, 3, 4, 2, 1, 6, 3, 2, 1, 5, 3, 3, 2, 4, 2, 2, 3, 0, 2, 1, 4, 5, 3, 3, 4, 4, 1, 2, 4, 5.

It is called as Discrete or ungrouped Frequency Distribution

62

Frequency DistributionFrequency DistributionGrouped frequency:

63

Frequency DistributionFrequency Distribution

Continuous Frequency distributionContinuous Frequency distribution when

variables are in continuous format there is need to

use continuous frequency distribution.

Say age of students: 4-6, 7-9, are not correct, instead of it:

Age in years:

Below 6,

6 or more but less than 9,

9 or more but less than 12, 64

Formation of Frequency Distribution: Continuous dataFormation of Frequency Distribution: Continuous data

1. Class Limit: These are the lowest and highest value(25-29)

2. Class Interval: the difference between upper and lower limit.

Here it is ‘4’.

3. Class of Frequency: the number of observation belonging to a

particular class is known as the frequency of that class.

4. Range: the difference between largest value and smallest value

is called the range and is denoted by ‘R’.

5. Class Mid-point = (Lower limit of the Class + Upper limit of the

Class)/2.

65

Types of Class IntervalsTypes of Class Intervals

1. Exclusive Method

2.Inclusive Method

3.Open-End Classes

66

Exclusive MethodExclusive Method

Profit earned by Companies

67

In this method the upper limit is exclusive and the item of that value is included in the next class.

Say in the above example Company earning 20 lakh profit will be included in the Class internal 20-30.

Inclusive MethodInclusive Method


68

In this method both upper limit and lower are included in the class.

Open-End classesOpen-End classes


69

A class limit is missing either at the lower end of the first class interval or at the upper end of the last class interval.

Charts &

Graphical Presentatio

n

Graphical PresentationGraphical Presentation

Charts & Graphics Charts & Graphics are visual aids which gives a

bird’s eye view of a given set of numerical data.

Important graphs are:

1. Histogram

2. Frequency Polygen

3. Frequency curve

4. Pie Chart

5. Bar diagram.

71

Class interval Frequency

0 – 20 13

20 – 40 18

40 – 60 25

60 – 80 15

80 – 100 9

Total 80 f

HistogramHistogram

HistogramHistogramA histogram is a graph that displays the data by using adjacent vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes.

A histogram is a simple (vertical) bar chart in which the frequency of observations within a class interval is represented by the corresponding bar.

The class intervals, and hence the width of the bars, will be of equal size

Frequency polygonFrequency polygonA frequency polygon is a line graph of a

grouped frequency distribution

It is constructed by marking the point on the top of each histogram bar at the midpoint of the class interval, then joining these points by straight lines

OgivesOgives

An ogive (or ogive curve) is the graphical

presentation of a cumulative frequency

distribution.

These ogives are classified as ‘less than’ and

‘more than ogives’.

Less than’, cumulative frequencies are plotted

against upper boundaries of their respective

class intervals.Grater than’ cumulative frequencies are plotted against lower boundaries of their respective class intervals.

OgivesOgivesFor Example:

Bar chartsBar chartsA bar chart consists of a series of

rectangular bars where the lengths of the bars represent the magnitudes of the respective quantities.

Types of Bar Diagrams:

1. Simple bar Diagrams

2. Multiple bar diagrams

3. Sub-divided or component bar diagram

4. Percentage bar diagrams

5. Deviation or Bilateral Diagrams.

Bar chartsBar charts1. Simple bar Diagrams

A simple bar diagram can be drawn using horizontal or vertical bar.

In business and economics, it is very a common diagram.

Vertical Bar Diagram

Bar chartsBar charts1. Simple bar Diagrams:

Horizontal Bar Diagram

Bar chartsBar chartsMultiple bar diagrams

Multiple bar diagram

provides more than one

phenomenon and highly

useful for direct comparison.

The bars are drawn

side-by-side and different

columns, shades can be

used for indicating each

variable used.

Bar chartsBar charts

Item of Expenditure

Family A (Income)

Family B (Income)

Food 1500 1500

Clothing 1250 600

Education 1250 900

Miscellaneous 1900 1000

Saving 1000 1000Total 6900 5000

Sub-Divided Bar

Diagram

In these bar diagram,

the bar is divided into

various parts in

proportion to the value

given in the data.

Bar chartsBar charts

Percentage Sub-

Divided Bar

Diagram

Here the components

are not the actual

values but the

percentage of the

whole.

Here each bar

represent 100

percent all bars are of

equal height.

Pie DiagramPie Diagram

Pie Diagram

Pie diagram helps us to show the

portioning of a total into its component parts.

It is used to show classes or groups of data

in proportion to whole data set. The entire pie

represents all the data, while each slice

represents a different class or group within

the whole.

Pie DiagramPie DiagramPie Diagram

Revenue collections for the year 2005-

2006 by government in Rs. (crore)s for

petroleum products are as follows. Draw the pie

diagram.

Pie DiagramPie Diagram

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