Introduction to Quantitative Techniques

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BirinderSingh,AssistantProfessor,PCTE
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COURSE – UNIT 1
 Introduction to statistics: Meaning, scope, importance
and limitations, applications of inferential statistics in
managerial decision-making.
 Analysis of data: Source of data, collection,
classification, tabulation, depiction of data.
 Measures of Central tendency: Arithmetic, weighted,
geometric mean, median and mode.
 Measures of Dispersion: Range, Quartile deviation,
Mean deviation, Standard deviation Coefficient of
variation, Skewness and Kurtosis 18
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COURSE – UNIT 2
 Sampling and Sampling Distribution: Concept
and definitions, census and sampling, probability
samples and non-probability samples, relationship
between sample size and errors, simple numerical
only.
 Hypothesis Testing: Sampling theory, Formulation
of Hypotheses, Application of Z-test, t-test, F-test
and Chi-Square test, Techniques of association of
attributes & testing. Test of significance for small
sample
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COURSE – UNIT 3
 Correlation Analysis: Significance, types, methods of
correlation analysis: Scatter diagrams, Graphic method,
Karl Pearson’s correlation co-efficient, Rank correlation
coefficient, Properties of Correlation.
 Regression analysis: meaning, application of
regression analysis, difference between correlation &
regression analysis, regression equations, standard error
and Regression coefficients.
 Index Number: Definition, and methods of construction,
tests of consistency, base shifting, splicing and deflation,
problems in construction and importance of index number.
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COURSE – UNIT 4
 Time Series Analysis: Meaning, Components and various
methods of time series analysis, Trend analysis: Least Square
method - Linear and Non- Linear equations, Applications in
business decision-making.
 Theory of Probability: Definition, basic concepts, events and
experiments, random variables, expected value, types of
probability, classical approach, relative frequency and subjective
approach to probability, theorems of probability, addition,
Multiplication and Bayes Theorem and its application.
 Theoretical Distributions: Difference
between frequency and probability distributions, Binomial,
Poisson and normal distribution
Note: Relevant Case Studies should be discussed in class
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STATISTICS
 It is set of procedures and rules…for reducing large
masses of data to manageable proportions and for
allowing us to draw conclusions from those data
 It helps businessmen in drawing inferences from
the available data and take the decisions
accordingly
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MEANING
 PLURAL SENSE – It refers to numerical statements
of facts relating to any field of enquiry such as data
relating to production, income, expenditure,
population, prices, etc.
 SINGULAR SENSE – It refers to a science in which
we deal with the techniques or methods for
collecting, classifying, presenting, analyzing and
interpreting the data.
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WHAT CAN STATS DO?
 Make data more manageable
 Group of numbers:
6, 1, 8, 3, 5, 4, 9
 Average is: 36/7 = 5.14
 Graphs:
0
10
20
30
40
50
60
70
80
90
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
East
West
North
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WHAT CAN STATS DO?
 Allow us to draw conclusions from the data
 Sachin’s Scores: 60, 100, 80, 30, 50
 Sachin’s Average is 350/5 = 70
 Sehwag’s Scores: 10, 150, 25, 5, 110
 Sehwag’s Average is 300/5 = 60
 Allows us to do this objectively and quantitatively
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APPLICATIONS OF STATISTICS IN DAY TO DAY LIFE
& IN BUSINESS
 Weather Forecasts
 Emergency Preparedness
 Political Campaigns
 Insurance
 Consumer Goods
 Family Budgets
 Consumer Goods
 Stock Market
 Quality Testing
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FEATURES OF STATISTICS AS SCIENCE
(STAGES OF STATISTICS)
Collection of Data
Organization of Data
Presentation of Data
Analysis of Data
Interpretation of Data
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SCOPE OF STATISTICS
Scope
Nature
Science Art
Subject
Matter
Descriptive
Statistics
Inferential
Statistics
Limitations
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FUNCTIONS OF STATISTICS
 To Present Facts in Definite Form
 Precision to the Facts
 Comparisons
 Forecasting
 Policy Making
 Enlarges Knowledge
 To Measure Uncertainty
 Establishes relationship between facts
 Helps other sciences in testing their laws
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IMPORTANCE OF STATISTICS
 Administrative Policies
 Industry/Business
 Agriculture
 Economics / Economic Planning
 Politicians
 Science & Research
 Banking & Insurance
 Education
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LIMITATIONS OF STATISTICS
 Study of numerical facts only
 Study of aggregates only
 Homogeneity of Data
 Can be used only be experts
 Qualitative Aspect Ignored
 It does not depict entire story of phenomenon
 Misuse of Statistics is possible
 Results are true only on average
 Statistical results are not always beyond doubt; only
means & not a solution
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TYPES OF DATA
Primary Data
• Data collected by the investigator for his own purpose,
for the first time. It is also called first hand data
• Primary data includes information collected from
interviews, experiments, surveys, questionnaires, focus
groups and measurements
Secondary Data
• It is widely available and obtained from another party. It
is also called second hand data
• Secondary data can be found in publications, journals
and newspapers.
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PRIMARY VS SECONDARY DATA
Basis for Comparison Primary Data Secondary Data
Data Real time data Past data
Process Very involved Quick and easy
Source
Surveys, observations,
experiments, questionnaire,
personal interview, etc.
Government publications,
websites, books, journal
articles, internal records etc.
Cost effectiveness Expensive Economical
Collection time Long Short
Specific
Always specific to the
researcher's needs.
May or may not be specific to
the researcher's need.
Available in Crude form Refined form
Accuracy and Reliability More Relatively less
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METHODS OF COLLECTING PRIMARY DATA
Observation Method
• Structured & Unstructured Observation
• Participant, Non Participant & Disguised Observation
• Controlled & Uncontrolled Observation
Interview Method
• Personal Interview
• Telephonic Interview
• Video Conferencing
Questionnaire
Schedules filled through Enumerators
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OBSERVATION METHOD
 The observation method is the most commonly used
method specially in studies relating to behavioral
science.
 Observation becomes a scientific tool and the method of
data collection for the researcher, when it serves a
formulated research purpose, is systematically planned
and recorded and is subjected to checks and controls
on validity and reliability.
 It is also a process of recording the behavior patterns of
people, objects, and occurrences without questioning or
communicating with them.
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OBSERVATION METHOD
 Structured Observation: This means observation of an
event personally by the observer when it takes place. This
method is flexible and allows the observer to see and record
subtle aspects of events and behaviour as they occur. He is
also free to shift places, change the focus of the observation.
Example: Observer is physically present to monitor
 Unstructured Observation: This does not involve
the physical presence of the observer, and the recording
is done by mechanical, photographic or electronic
devices. Example : Recording customer and employee
movements by a special motion picture camera
mounted in a department of large store.
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OBSERVATION METHOD
 Participant Observation: In this observation, the
observer is a part of the phenomenon or group
which observed and he acts as both an observer
and a participant.
Example: a study of tribal customs by an
anthropologist by taking part in tribal activities like folk
dance. The person who are observed should not be
aware of the researcher’s purpose. Then only their
behaviour will be ‘natural.’
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OBSERVATION METHOD
 Non - Participant Observation: In this method, the
observer stands apart and does not participate in
the phenomenon observed. Naturally, there is no
emotional involvement on the part of the observer.
This method calls for skill in recording observations
in an unnoticed manner.
Example: Use of recording devices to examine the
details of how people talk and behave together.
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OBSERVATION METHOD
 Disguised Observation: In this method, the
observer observes in such a manner that his
presence is unknown to the people he is observing.
Example: Investigation done in Police Custody
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OBSERVATION METHOD
 Controlled Observation: Controlled observation is
carried out either in the laboratory or in the field. It is
typified by clear and explicit decisions on what, how, and
when to observe. It is primarily used for inferring
causality, and testing casual hypothesis.
 Uncontrolled Observation: This does not involve
over extrinsic and intrinsic variables. It is primarily used
for descriptive research. Participant observation is a
typical uncontrolled one.
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OBSERVATION METHODS
 Not Biased
 Data is not affected by
past behavior
 Natural behavior of the
group can be recorded
 Expensive
 Limited Information
 Unforeseen factors
may interfere with the
observational task
Merits Demerits
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INTERVIEW METHOD
 Personal Interview: It is a face to face two way
communication between the interviewer and the
respondents. Generally the personal interview is
carried out in a planned manner and is referred to
as ‘structured interview’. This can be done in many
forms e.g. door to door or as a planned formal
executive meeting.
 Telephonic Interview: the information is collected
from the respondent by asking him questions on the
phone is called as telephone interview.
 Video Conferencing: The combination of video
camera and computer is used for conducting this
interview.
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INTERVIEW METHOD
 Accuracy of data
 Reliability of data
 Flexibility of questions
 Originality of data
 Biased
 Costly
 Not proper for wide
areas
 Wrong Conclusions
Merits Demerits
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QUESTIONNAIRE
 In this method, a list of questions relating to the
survey is prepared.
 It can be sent to the interviewee in the following
ways:
o Through post
o Through E Mail
o Through personal presence
o Online Surveys
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QUESTIONNAIRE
 Economical
 Originality of data
 Wider Area
 Lack of Interest
 Lack of flexibility
 Limited use
 Biased
 Less Accuracy
Merits Demerits
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QUALITIES OF A GOOD QUESTIONNAIRE
 Limited number of questions
 Simplicity
 Proper Order of the Questions
 No Undesirable Questions
 Avoid Calculations
 Pre testing
 Clear Instructions
 Cross Verifications of Questions
 Request for return
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SECONDARY DATA
 Government / Semi
Government Publications
 Reports of Committees &
Commissions
 Publications of Trade
Associations
 Publications of Research
Associations
 Journals & Papers
 Publications of Research
Scholars
 International Publications
 These data are collected
by the government &
private organizations and
is not published. These
are used as secondary
data too.
Published Sources Unpublished Sources
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CLASSIFICATION OF DATA
 It is the process of arranging the data into different
classes or groups according to their common
characteristics.
 According to Spurr & Smith, “Classification is the
grouping of related facts into classes”
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OBJECTIVES OF CLASSIFICATION
 To make comparisons
 To arrange the data in such a way that their
similarities and dissimilarities become very clear
 To point out the most important features of the data
at a glance
 To present the data in a brief form
 To enable statistical treatment of the collected data
 To make data attractive and effective
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METHODS OF CLASSIFICATION
Geographical Classification
Chronological Classification
Qualitative Classification
Quantitative Classification
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GEOGRAPHICAL CLASSIFICATION
Number of Colleges in 2016
Punjab 70
Haryana 30
Jammu & Kashmir 20
Himachal Pradesh 25
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CHRONOLOGICAL CLASSIFICATION
Population of India (in Cr.)
Year 1971 54.8
Year 1981 68.4
Year 1991 84.4
Year 2001 102.8
Year 2011 121.0
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QUALITATIVE CLASSIFICATION
 In this, data are classified on the basis of some
attribute or quality such as sex, literacy, religion etc.
 It is of two types:
 Simple Classification: When only one attribute is
studied i.e. Classification of population on the
basis of Male & Female
 Manifold Classification: When more than one
attribute is studied i.e. Classification of population
on the basis of Male & Female along with Rural &
Urban.
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QUANTITATIVE CLASSIFICATION
 When data are classified on the basis of some
characteristics which is capable of direct
quantitative measurement such as height, weight,
income, marks etc.
 It is also called numerical or grouped classification
Weight (in kgs.) No. of persons
70-80 50
80-90 30
90-100 15
100-110 5
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QUANTITATIVE CLASSIFICATION
Variable
• Characteristic capable
of direct quantitative
measurement
• Eg. Height, Weight,
Marks, Production,
Consumption etc.
Frequency
• It is the quantity linked
with the variable
• Eg. No. of persons in
weight range 70-80
kgs is 50
Weight
(in kgs.)
No. of
persons
70-80 50
80-90 30
90-100 15
100-110 5
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FREQUENCY DISTRIBUTION
Marks No. of students
10 5
12 6
15 10
18 3
20 1
Discrete Frequency
Distribution
Grouped Frequency
Distribution
Marks: Out of 20
Total Students: 25
0-20 1
20-40 6
40-60 10
60-80 5
80-100 3
Marks: Out of 100
Total Students: 25
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TERMINOLOGY ASSOCIATED WITH GROUPED
 Class Interval/Class: Its
group of numbers in which
items are placed. Eg. 0-20,
20-40, 40-60 etc.
 Class Frequency (f): The
number of observation
falling within a class. Eg.
“10” against 40-60
 Class Limits: Each class is
located between two limits.
The lower value of a class is
called lower limit & higher
value is called upper limit.
Eg. In 10-20: 10 is LL (l1) &
20 is UL.(l2)
0-20 1
20-40 6
40-60 10
60-80 5
80-100 3
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TERMINOLOGY ASSOCIATED WITH GROUPED
 Class Mark/ Mid
Value: It is the average
value of l1 & l2. MV = (l1
+ l2)/2
 Class Size: The width
or class size or
magnitude of a class is
the difference between
its lower and upper
class limits. It is
denoted by i= l2 – l1
0-20 1
20-40 6
40-60 10
60-80 5
80-100 3
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TYPES OF SERIES IN GROUPED FREQUENCY
DISTRIBUTION
Exclusive
Series
Inclusive
Series
Open End
Series
Mid Value
Series
Cumulative
Frequency
Series
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EXCLUSIVE SERIES
0-20 1
20-40 6
40-60 10
60-80 5
80-100 3
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INCLUSIVE SERIES
Marks Frequency
10-14 4
15-19 5
20-24 8
25-29 5
30-34 4
Total 26
Marks Frequency
9.5-14.5 4
14.5-19.5 5
19.5-24.5 8
24.5-29.5 5
29.5-34.5 4
Total 26
Inclusive Series To Exclusive Series
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OPEN ENDED SERIES
Marks Frequency
Less than 5 4
5-10 5
10-15 8
15-20 5
20 and above 4
Total 26
Marks Frequency
0-5 4
5-10 5
10-15 8
15-20 5
20-25 4
Total 26
Open Ended Series To Exclusive Series
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FREQUENCY SERIES CONTAINING
MID VALUE
Mid Value Frequency
5 4
15 5
25 8
35 5
45 4
Total 26
Marks Frequency
0-10 4
10-20 5
20-30 8
30-40 5
40-50 4
Total 26
Mid Value Series To Exclusive Series
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CUMULATIVE FREQUENCY SERIES
Marks Frequency
Less than 10 4
Less than 20 20
Less than 30 40
Less than 40 48
Less than 50 50
Marks Frequency
0-10 4
10-20 20 – 4 = 16
20-30 40 – 20 = 20
30-40 48 – 40 = 8
40-50 50 – 48 = 2
Total 50
Less Than Type Series To Exclusive Series
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CUMULATIVE FREQUENCY SERIES
Marks Frequency
More than 0 50
More than 20 48
More than 40 40
More than 60 20
More than 80 6
Marks Frequency
0-20 50 – 48 = 2
20-40 48 – 40 = 8
40-60 40 – 20 = 20
60-80 20 – 6 = 14
80-100 6
Total 50
More Than Type Series To Exclusive Series
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INTRODUCTION
 Whenever verbal problems involving a certain
situation is presented visually before the learners, it
makes easier for the learner to understand the
problem and attempt its solution.
 Similarly, when the data are presented pictorially (or
graphically) before the learners, it makes the
presentation eye-catching and more intelligible.
 The learners can easily see the salient features of
the data and interpret them.
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INVENTOR OF GRAPHS
 William Playfair (1759-1823), Scottish engineer and
political economist, is the principal inventor of
statistical graphs.
 In 1786, he published “Commercial and Political
Atlas” that contained 44 charts.
 He invented three of the four basic forms of graph:
o The statistical line graph
o The bar graph
o The pie graph
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TYPES OF GRAPHS
 Line graphs
-Polygraph
 Bar graphs
 Pie graphs
 Flow Charts
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LINE GRAPH
 The line graphs are usually drawn to represent the
time series data
Example: temperature, rainfall, population growth,
birth rates and the death rates.
1000
1500
1750
1250
1000
2000
0
500
1000
1500
2000
2500
2011 2012 2013 2014 2015 2016
P
r
i
c
e
Year
Share Price of Co. ABC Ltd.
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20
18
19
10
18
20
17
15
16
15
0
5
10
15
20
25
Test 1 Test 2 Test 3 Test 4 Test 5
Comparative Score Card
Ashima Dhruv
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LINE GRAPH
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1.2. POLYGRAPH
• Polygraph is a line graph in which two or more than
two variables are shown on a same diagram by
different lines. It helps in comparing the data.
Examples which can be shown as polygraph are:
– The growth rate of different crops like rice, wheat,
pulses in one diagram.
– The birth rates, death rates and life expectancy in one
diagram.
– Sex ratio in different states or countries in one diagram.
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POLYGRAPH
1000
1500
1750
1250
1000
2000
375
625
750
55
450
850
1500
1600
1800
1600
1500
1900
0
500
1000
1500
2000
2500
2011 2012 2013 2014 2015 2016
P
r
i
c
e
Year
Share Price of 3 Companies
ABC Ltd. XYZ Ltd. PQR Ltd.
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POLYGRAPH
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BAR GRAPHS
It is also called a columnar diagram. The bar
diagrams are drawn through columns of equal width.
Following rules were observed while constructing a
bar diagram:
(a) The width of all the bars or columns is similar.
(b) All the bars should be placed on equal
intervals/distance.
(c) Bars are shaded with colors or patterns to make
them distinct and attractive.
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TYPES OF BAR GRAPHS
 Three types of Bar Graphs are used to represent
different data sets:
o The simple bar diagram
o Compound bar diagram
o Polybar diagram
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THE SIMPLE BAR DIAGRAM
 A simple bar diagram is constructed for an
immediate comparison. It is advisable to arrange
the given data set in an ascending or descending
order and plot the data variables accordingly.
However, time series data are represented
according to the sequencing of the time period.
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8
14
16
25
32
37
34
32
30
26
20
14
0
5
10
15
20
25
30
35
40
Temperature (in C)
Temperature (in C)
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THE SIMPLE BAR DIAGRAM
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COMPOUND BAR DIAGRAM
 When different components are grouped in one set
of variable or different variables of one component
are put together, their representation is made by a
compound bar diagram. In this method, different
variables are shown in a single bar with different
rectangles.
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COMPOUND BAR GRAPH
0
50
100
150
200
250
300
2013 2014 2015 2016
80 75 85 100
85 81
88
90
90
82
95
100
Scoresachievedineachsubject
Year
Subject A Subject B Subject C
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COMPOUND BAR DIAGRAM
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POLYBAR DIAGRAM
 The line and bar graphs as drawn separately may
also be combined to depict the data related to some
of the closely associated characteristics such as the
climatic data of mean monthly temperatures and
rainfall.
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POLYBAR DIAGRAM
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PIE GRAPHS
 Pie diagram is another graphical method of the
representation of data. It is drawn to depict the total
value of the given attribute using a circle. Dividing
the circle into corresponding degrees of angle then
represent the sub– sets of the data. Hence, it is
also called as Divided Circle Diagram.
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PIE CHART
29%
23%
22%
26%
Sales in Cr. of ABC Ltd. in 2015-16
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
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PIE GRAPHS
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FLOW MAPS/CHART
 Flow chart is a combination of graph and map. It is
drawn to show the flow of commodities or people
between the places of origin and destination. It is
also called as Dynamic Map.
 Transport map, which shows number of
passengers, vehicles, etc., is the best example of a
flow chart.
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CONCLUSION
 If the information is presented in tabular form or in a
descriptive record, it becomes difficult to draw
results.
 Graphical form makes it possible to easily draw
visual impressions of data.
 The graphic method of the representation of data
enhances our understanding.
 It makes the comparisons easy.
 Besides, such methods create an imprint on mind
for a longer time
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Introduction to Quantitative Techniques

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