511035200 mb0050 research methodology

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 Name: Shailesh Kumar Registration Number: 511035200 Semester: 3 rd Specialized Stream: Information Systems Management  MBA SEMESTER III MB0050  Research Methodology- 4 Credits  Assignment Set- 1 (60 Marks)  Question 1: Why should a manger know about research when the job entails managing people, products, events, environments, and the like?  Answer: Research simply means a search for facts answers to questions and solutions to problems. It is a purposive investigation. It is an organized inquiry. It seeks to find explanations to unexplained phenomenon to clarify the doubtful facts and to correct the misconceived facts. Research is the organized and systematic inquiry or investigation which provides information for solving a problem or finding answers to a complex issue. Research in business: Often, organization members want to know everything about their products, services, programs, etc. Your research plans depend on what information you need to collect in order to make major decisions about a product, service, program, etc. Research provides the needed information that guides managers to make informed decisions to successfully deal with problems. The more focused you are about your resources, products, events and environments what you want to gain by your research, the more effective and efficient you can be in your research, the shorter the time it will take you and ultimately the less it will cost you. Manager’s role in research programs of a company:  Managing people is only a fraction of a manager's responsibility - they have to manage the operations of the department, and often have responsibilities towards the profitability of the organization. Knowledge of research can be very helpful for a good manager. Question 2: a. How do you evolve research design for exploratory research? Briefly analyze. b. Briefly explain Independent, dependent and extraneous variables in a research design.  Answer: a. Research design for e xploratory research: Research simply means a search for facts answers to questions and solutions to problems. It is a purposive investigation. It is an organized inquiry. It seeks to find explanations to unexplained phenomenon to clarify the doubtful facts and to correct the misconceived facts. Although any typology of research is inevitably arbitrary, Research may be classified crudely according to its major intent or the methods. It is also known as formulating research. It is preliminary study of an unfamiliar problem about which the researcher has little or no knowledge. It is ill-structured and much less focused on pre- determined objectives. It usually takes the form of a pilot study. The purpose of this research may

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8/3/2019 511035200 MB0050 Research Methodology

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Name: Shailesh Kumar Registration Number: 511035200 Semester: 3rd

Specialized Stream: Information Systems Management 

MBA SEMESTER III MB0050 – Research Methodology- 4 Credits 

Assignment Set- 1 (60 Marks) 

Question 1: Why should a manger know about research when the job entails managing people,

products, events, environments, and the like?

 Answer:

Research simply means a search for facts – answers to questions and solutions to problems. It is a

purposive investigation. It is an organized inquiry. It seeks to find explanations to unexplained

phenomenon to clarify the doubtful facts and to correct the misconceived facts. Research is the

organized and systematic inquiry or investigation which provides information for solving a problem or

finding answers to a complex issue.

Research in business:

Often, organization members want to know everything about their products, services, programs, etc.

Your research plans depend on what information you need to collect in order to make major decisions

about a product, service, program, etc. Research provides the needed information that guides

managers to make informed decisions to successfully deal with problems.

The more focused you are about your resources, products, events and environments what you want to

gain by your research, the more effective and efficient you can be in your research, the shorter the time

it will take you and ultimately the less it will cost you.

Manager’s role in research programs of a company: 

Managing people is only a fraction of a manager's responsibility - they have to manage the operationsof the department, and often have responsibilities towards the profitability of the organization.

Knowledge of research can be very helpful for a good manager.

Question 2:

a.  How do you evolve research design for exploratory research? Briefly analyze.

b.  Briefly explain Independent, dependent and extraneous variables in a research design.

 Answer: 

a.  Research design for exploratory research:

Research simply means a search for facts – answers to questions and solutions to problems. It is a

purposive investigation. It is an organized inquiry. It seeks to find explanations to unexplained

phenomenon to clarify the doubtful facts and to correct the misconceived facts. Although any

typology of research is inevitably arbitrary, Research may be classified crudely according to its

major intent or the methods.

It is also known as formulating research. It is preliminary study of an unfamiliar problem about 

which the researcher has little or no knowledge. It is ill-structured and much less focused on pre-

determined objectives. It usually takes the form of a pilot study. The purpose of this research may

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Name: Shailesh Kumar Registration Number: 511035200 Semester: 3rd

Specialized Stream: Information Systems Management 

be to generate new ideas, or to increase the researcher’s familiarity with the problem or to make a

precise formulation of the problem or to gather information for clarifying concepts or to

determine whether it is feasible to attempt the study. Katz conceptualizes two levels of 

exploratory studies. “At the first level is the discovery of the significant variable in the situations;

at the second, the discovery of relationships between variables.” 

b.  Independent and dependent and extraneous variables in a research design:

The research designer understandably cannot hold all his decisions in his head. Even if he could,

he would have difficulty in understanding how these are inter-related. Therefore, he records his

decisions on paper or record disc by using relevant symbols or concepts. Such a symbolic

construction may be called the research design or model. A research design is a logical and

systematic plan prepared for directing a research study. 

Dependent and Independent variables:

A magnitude that varies is known as a variable. The concept may assume different quantitative

values, like height, weight, income, etc. Qualitative variables are not quantifiable in the strictest 

sense of objectivity. However, the qualitative phenomena may also be quantified in terms of thepresence or absence of the attribute considered. Phenomena that assume different values

quantitatively even in decimal points are known as „continuous variables ‟. But, all variables need

not be continuous. Values that can be expressed only in integer values are called „non -continuous

variables ‟. In statistical term, they are also known as „discrete variable  ‟. For example, age is a

continuous variable; whereas the number of children is a non-continuous variable. When changes

in one variable depends upon the changes in one or more other variables, it is known as a

dependent or endogenous variable, and the variables that cause the changes in the dependent 

variable are known as the independent or explanatory or exogenous variables. For example, if 

demand depends upon price, then demand is a dependent variable, while price is the independent 

variable.

And if, more variables determine demand, like income and prices of substitute commodity, thendemand also depends upon them in addition to the own price. Then, demand is a dependent 

variable which is determined by the independent variables like own price, income and price of 

substitute.

Extraneous variable:

The independent variables which are not directly related to the purpose of the study but affect the

dependent variable are known as extraneous variables. For instance, assume that a researcher

wants to test the hypothesis that there is relationship between children’s school performance andtheir self-concepts, in which case the latter is an independent variable and the former, the

dependent variable. In this context, intelligence may also influence the school performance.

However, since it is not directly related to the purpose of the study undertaken by the researcher,it would be known as an extraneous variable. The influence caused by the extraneous variable on

the dependent variable is technically called as an „experimental error  ‟. Therefore, a research

study should always be framed in such a manner that the dependent variable completely

influences the change in the independent variable and any other extraneous variable or variables.

Question 3:

a.  Differentiate between ‘Census survey’ and ‘ Sample Survey’ 

b.   Analyse multi-stage and sequential sampling.

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Name: Shailesh Kumar Registration Number: 511035200 Semester: 3rd

Specialized Stream: Information Systems Management 

 Answer:

a.  Difference between Census survey and Sample Survey

Census Survey  Sample SurveyA census measures absolutely everyone in the

whole country. This obviously means that a

census survey is a much bigger exercise in

nature and procedures

A part of the population is known as sample

Census survey also is a very time consuming

exercise as information needs to be collected

from each and every individual from the

population.

On the other hand, sample survey is easier as

a representative sample is taken from the

population and the results obtained are

extrapolated to fit the entire population.

There are times and requirements where

governments have to indulge in censussurvey even if it is time consuming and very

expensive as it needs to formulate policies

and welfare programs for the population. For

example, when a government has to count 

heads of the population

Sample surveys cannot count the number of 

people in the country but when government is planning on a welfare program for cancer

patients, it can conduct a sample survey of 

some of the cancer patients and then

extrapolate the results on the section of the

population that is undergoing treatment for

cancer.

Census survey is more accurate. there is margin for error in sample survey

b.   Analyse multi-stage and sequential sampling: 

Multi-stage sampling:

In multi-stage sampling method, sampling is carried out in two or more stages. The population is

regarded as being composed of a number of second stage units and so forth. That is, at each stage, a

sampling unit is a cluster of the sampling units of the subsequent stage. First, a sample of the first stage

sampling units is drawn, then from each of the selected first stage sampling unit, a sample of the second

stage sampling units is drawn. The procedure continues down to the final sampling units or population

elements. Appropriate random sampling method is adopted at each stage. It is appropriate where the

population is scattered over a wider geographical area and no frame or list is available for sampling. It 

is also useful when a survey has to be made within a limited time and cost budget. The major

disadvantage is that the procedure of estimating sampling error and cost advantage is complicated.

Sequential sampling: 

Sequential sampling is a non-probability sampling technique wherein the researcher picks a single or a

group of subjects in a given time interval, conducts his study, analyses the results then picks another

group of subjects if needed and so on. This sampling technique gives the researcher limitless chances of 

fine tuning his research methods and gaining a vital insight into the study that he is currently pursuing.

There is very little effort in the part of the researcher when performing this sampling technique. It is

not expensive, not time consuming and not workforce extensive.

This sampling method is hardly representative of the entire population. Its only hope of approaching

representativeness is when the researcher chose to use a very large sample size significant enough to

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Name: Shailesh Kumar Registration Number: 511035200 Semester: 3rd

Specialized Stream: Information Systems Management 

represent a big fraction of the entire population. Due to the aforementioned disadvantages, results

from this sampling technique cannot be used to create conclusions and interpretations pertaining to

the entire population.

Question 4: List down various measures of central tendency and explain the difference betweenthem?

 Answer:

Measures of Central Tendency:

The term central tendency refers to the "middle" value or perhaps a typical value of the data, and is

measured using the mean, median, or mode. Each of these measures is calculated differently, and the

one that is best to use depends upon the situation.

Analysis of data involves understanding of the characteristics of the data. The following are the

important characteristics of a statistical data:

  Central tendency

  Dispersion

  Skew ness

  Kurtosis

In a data distribution, the individual items may have a tendency to come to a central position or an

average value. For instance, in a mark distribution, the individual students may score marks between

zero and hundred. In this distribution, many students may score marks, which are near to the average

marks, i.e. 50. Such a tendency of the data to concentrate to the central position of the distribution is

called central tendency. Central tendency of the data is measured by statistical averages. Averages areclassified into two groups.

1. Mathematical averages

2. Positional averages

Statistical Averages

Mathematical averages Positional averages

Arithmetic mean Median

Geometric mean Mode

Harmonic mean

Arithmetic mean, geometric mean and harmonic mean are mathematical averages. Median and mode

are positional averages. These statistical measures try to understand how individual values in a

distribution concentrate to a central value like average. If the values of distribution approximately

come near to the average value, we conclude that the distribution has central tendency.

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Specialized Stream: Information Systems Management 

Difference between Mean and Median:

Mean (Mathematical averages) Median (Positional averages)

When the sample size is large and does not 

include outliers, the mean score usually

provides a better measure of central

tendency.

The median may be a better indicator of the

most typical value if a set of scores has an

outlier. An outlier is an extreme value that 

differs greatly from other values.The mean is the most commonly-used

measure of central tendency. When we talk 

about an "average", we usually are referring

to the mean

The median often is used when there are a

few extreme values that could greatly

influence the mean and distort what might be

considered typical.

The mean is simply the sum of the values

divided by the total number of items in the

set 

The median is determined by sorting the data

set from lowest to highest values and taking

the data point in the middle of the sequence

Question 5: Select any topic for research and explain how you will use both secondary and

primary sources to gather the required information.

 Answer:

For performing research on the literacy levels among families, the primary and secondary sources of 

data can be used very effectively. More specifically the primary sources of data collection is suggested

in this regard. Because personal data or data related to human beings consist of:

1. Demographic and socio-economic characteristics of individuals: Age, sex, race, social class, religion,

marital status, education, occupation income, family size, location of the household life style etc.

2. Behavioral variables: Attitudes, opinions, awareness, knowledge, practice, intentions, etc.

3. Organizational data consist of data relating to an organizations origin, ownership, objectives,

resources, functions, performance and growth.4. Territorial data are related to geo-physical characteristics, resource endowment, population,

occupational pattern infrastructure degree of development, etc. of spatial divisions like villages, cities,

talluks, districts, state and the nation.

The data serve as the bases or raw materials for analysis. Without an analysis of factual data, no

specific inferences can be drawn on the questions under study. Inferences based on imagination or

guess work cannot provide correct answers to research questions. The relevance, adequacy and

reliability of data determine the quality of the findings of a study.

Data form the basis for testing the hypothesis formulated in a study. Data also provide the facts and

figures required for constructing measurement scales and tables, which are analyzed with statistical

techniques. Inferences on the results of statistical analysis and tests of significance provide the answersto research questions. Thus, the scientific process of measurements, analysis, testing and inferences

depends on the availability of relevant data and their accuracy. Hence, the importance of data for any

research studies

The sources of data may be classified into:

a.  Primary sources

b.  Secondary sources.

Primary Sources of Data:

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Name: Shailesh Kumar Registration Number: 511035200 Semester: 3rd

Specialized Stream: Information Systems Management 

Primary sources are original sources from which the researcher directly collects data that have not 

been previously collected e.g.., collection of data directly by the researcher on brand awareness, brand

preference, brand loyalty and other aspects of consumer behaviour from as ample of consumers by

interviewing them,. Primary data are first-hand information collected through various methods such as

observation, interviewing, mailing etc.

 Advantage of Primary Data:

  It is original source of data

  It is possible to capture the changes occurring in the course of time.

  It flexible to the advantage of researcher.

  Extensive research study is based of primary data

Disadvantage of Primary Data:

  Primary data is expensive to obtain

  It is time consuming

  It requires extensive research personnel who are skilled.

  It is difficult to administer

Methods of Collecting Primary Data:

Primary data are directly collected by the researcher from their original sources. In this case, the

researcher can collect the required date precisely according to his research needs, he can collect them

when he wants them and in the form he needs them. But the collection of primary data is costly and

time consuming. Yet, for several types of social science research required data are not available from

secondary sources and they have to be directly gathered from the primary sources. In such cases where

the available data are in appropriate, inadequate or obsolete, primary data have to be gathered. They

include: socioeconomic surveys, social anthropological studies of rural communities and tribal

communities, sociological studies of social problems and social institutions. Marketing research,

leadership studies, opinion polls, attitudinal surveys, readership, radio listening and T.V. viewing

surveys, knowledge-awareness practice (KAP) studies, farm managements studies, businessmanagement studies etc. There are various methods of data collection. A ‘Method’ is different from a

‘Tool’ while a method refers to the way or mode of gathering data, a tool is an instruments used for themethod. For example, a schedule is used for interviewing. The important methods are (a) observation,

(b) interviewing,(c)mail survey,(d)experimentation,(e) simulation and (f) projective technique. Each of 

these methods is discussed in detail in the subsequent sections in the later chapters.

Secondary Sources of Data:

These are sources containing data which have been collected and compiled for another purpose. The

secondary sources consists of readily compendia and already compiled statistical statements and

reports whose data may be used by researchers for their studies e.g., census reports , annual reports

and financial statements of companies, Statistical statement, Reports of Government Departments,Annual reports of currency and finance published by the Reserve Bank of India, Statistical statements

relating to Co-operatives and Regional Banks, published by the NABARD, Reports of the National

sample survey Organization, Reports of trade associations, publications of international organizations

such as UNO, IMF, World Bank, ILO, WHO, etc., Trade and Financial journals newspapers etc.

Secondary sources consist of not only published records and reports, but also unpublished records.

The latter category includes various records and registers maintained by the firms and organizations,

e.g., accounting and financial records, personnel records, register of members, minutes of meetings,

inventory records etc.

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Features of Secondary Sources:

Though secondary sources are diverse and consist of all sorts of materials, they have certain common

characteristics. First, they are readymade and readily available, and do not require the trouble of 

constructing tools and administering them

Second, they consist of data which a researcher has no original control over collection andclassification. Both the form and the content of secondary sources are shaped by others. Clearly, this is

a feature which can limit the research value of secondary sources. Finally, secondary sources are not 

limited in time and space. That is, the researcher using them need not have been present when and

where they were gathered

Use of Secondary Data:

The second data may be used in three ways by a researcher. First, some specific information from

secondary sources may be used for reference purpose. For example, the general statistical information

in the number of co-operative credit societies in the country, their coverage of villages, their capital

structure, volume of business etc., may be taken from published reports and quoted as background

information in a study on the evaluation of performance of cooperative credit societies in a selecteddistrict/state.

Second, secondary data may be used as bench marks against which the findings of research maybe

tested, e.g., the findings of a local or regional survey may be compared with the national averages; the

performance indicators of a particular bank may be tested against the corresponding indicators of the

banking industry as a whole; and so on.

Finally, secondary data may be used as the sole source of information for a research project. Such

studies as securities Market Behaviour, Financial Analysis of companies, Trade in credit allocation in

commercial banks, sociological studies on crimes, historical studies, and the like, depend primarily on

secondary data. Year books, statistical reports of government departments, report of public

organizations of Bureau of Public Enterprises, Censes Reports etc., and serve as major data sources forsuch research studies

 Advantages of Secondary Data:

Secondary sources have some advantages:

  Secondary data, if available can be secured quickly and cheaply. Once their source of 

documents and reports are located, collection of data is just matter of desk work. Event he

tediousness of copying the data from the source can now be avoided, thanks to Xeroxing

facilities.

  Wider geographical area and longer reference period may be covered without much cost. Thus,

the use of secondary data extends the researcher’s space and time reach.   The use of secondary data broadens the data base from which scientific generalizations can be

made.

  Environmental and cultural settings are required for the study.

  The use of secondary data enables a researcher to verify the findings bases on primary data. It 

readily meets the need for additional empirical support. The researcher needs not wait the time

when additional primary data can be collected.

Disadvantages of Secondary Data:

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The use of a secondary data has its own limitations.

  The most important limitation is the available data may not meet our specific needs. The

definitions adopted by those who collected those data may be different; units of measure may

not match; and time periods may also be different.

  The available data may not be as accurate as desired. To assess their accuracy we need to know

how the data were collected.  The secondary data are not up-to-date and become obsolete when they appear in print, because

of time lag in producing them. For example, population census data are published two or three

years later after compilation and no new figures will be available for another ten years.

  Finally, information about the whereabouts of sources may not be available to all social

scientists. Even if the location of the source is known, the accessibility depends primarily on

proximity. For example, most of the unpublished official records and compilations are located

in the capital city, and they are not within the easy reach of researchers based in far off places.

Evaluation of Secondary Data:

When a researcher wants to use secondary data for his research, he should evaluate them before

deciding to use them.

1)  Data Pertinence:

  The first consideration in evaluation is to examine the pertinence of the available secondary

data to the research problem under study. The following questions should be considered.

  What are the definitions and classifications employed? Are they consistent?

  What are the measurements of variables used? What is the degree to which they conform to the

requirements of our research?

On the basis of above consideration, the pertinence of the secondary data to the research on hand

should be determined, as a researcher who is imaginative and flexible may be able to redefine his

research problem so as to make use of otherwise unusable available data.

2)  Data Quality:

If the researcher is convinced about the available secondary data for his needs, the next step is to

examine the quality of the data. The quality of data refers to their accuracy, reliability and

completeness. The assurance and reliability of the available secondary data depends on the

organization which collected them and the purpose for which they were collected. What is the

authority and prestige of the organization? Is it well recognized? Is it noted for reliability? It is capable

of collecting reliable data? Does it use trained and well qualified investigators? The answers to these

questions determine the degree of confidence we can have in the data and their accuracy. It is

important to go to the original source of the secondary data rather than to use an immediate source

which has quoted from the original. Then only, the researcher can review the cautionary and othercomments that were made in the original source.

3)  Data Completeness:

The completeness refers to the actual coverage of the published data. This depends on the

methodology and sampling design adopted by the original organization. Is the methodology sound? Is

the sample size small or large? Is the sampling method appropriate? Answers to these questions may

indicate the appropriateness and adequacy of the data for the problem under study. The question of 

possible bias should also be examined. Whether the purpose for which the original organization

collected the data had a particular orientation? Has the study been made to promote the organization’s

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own interest? How the study was conducted? These are important clues. The researcher must be on

guard when the source does not report the methodology and sampling design. Then it is not possible to

determine the adequacy of the secondary data for the researcher’s study. 

Question 6:a.  Explain the role of Graphs and Diagrams?

b.  What are the Types and General rules for graphical representation of data?

 Answer:

a)  Role of Graphs and Diagrams:

In presenting the data of frequency distributions and statistical computations, it is often desirable to

use appropriate forms of graphic presentations. In additions to tabular forms, graphic presentation

involves use of graphics, charts and other pictorial devices such as diagrams. These forms and devices

reduce large masses of statistical data to a form that can be quickly understood at the glance. The

meaning of figures in tabular form may be difficult for the mind to grasp or retain. “Properlyconstructed graphs and charts relieve the mind of burdensome details by portraying facts concisely,

logically and simply.” They, by emphasizing new and significant relationship, are also useful in

discovering new facts and in developing hypothesis.

The device of graphic presentation is particularly useful when the prospective readers are non-

technical people or general public. It is useful to even technical people for dramatizing certain points

about data; for important points can be more effectively captured in pictures than in tables. However,

graphic forms are not substitutes for tables, but are additional tools for the researcher to emphasize

the research findings.

Graphic presentation must be planned with utmost care and diligence. Graphic forms used should be

simple, clear and accurate and also be appropriate to the data. In planning this work, the followingquestions must be considered.

a.  What is the purpose of the diagram?

b.  What facts are to be emphasized?

c.  What is the educational level of the audience?

d.  How much time is available for the preparation of the diagram?

e.  What kind of chart will portray the data most clearly and accurately?

Role of Graphs:

Because graphs provide a compact, rhetorically powerful way of representing research findings, recent theories of science have postulated their use as a distinguishing feature of science. Studies have shown

that the use of graphs in journal articles correlates highly with the hardness of scientific fields, both

across disciplines and across subfields of psychology.

Role of Diagrams:

Recent technological advances have enabled the large-scale adoption of diagrams in a diverse range of 

areas. Increasingly sophisticated visual representations are emerging and, to enable effective

communication, insight is required into how diagrams are used and when they are appropriate for use.

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The pervasive, everyday use of diagrams for communicating information and ideas serves to illustrate

the importance of providing a sound understanding of the role that diagrams can, and do, play.

Research in the field of diagrams aims to improve our understanding of the role of diagrams, sketches

and other visualizations in communication, computation, cognition, creative thought, and problem

solving. These concerns have triggered a surge of interest in the study of diagrams.

The study of diagrammatic communication as a whole must be pursued as an interdisciplinaryendeavor. Diagrams attract a large number of researchers from virtually all related fields, placing the

conference as a major international event in the area.

b)  Types and General rules for graphical representation of data:

Graphical representation is done of the data available. This is very important step of statistical analysis.

We will be discussing the organization of data. The word 'Data' is plural for 'datum'; datum means

facts. Statistically the term is used for numerical facts such as measures of height, weight and scores on

achievement and intelligence tests.

Graphs and diagram leave a lasting impression on the mind and make intelligible and easily

understandable the salient features of the data. Forecasting also becomes easier with the help of graph.Thus it is of interest to study the graphical representation of data.

The graphical representation of data is categorized as basic five types:

1)  Bar graph

2)  Pie graph

3)  Line graph

4)  Scatter plot 

5)  Histogram

Examples of graphical representation of data:

Let us see some examples of graphical representation of data.

1)  Bar chart: 

A Bar chart (or diagram) is a graphical representation of data using bars (rectangles of same width).

It is one dimensional in which case only the height of the rectangle matters. 

 year  1931 1941 1951 1961 1971 1981

 populationof a place 

6000 7600 8900 12000 13500 18000

 Solution: scale: Y axis 1 cm = 1000 years

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2)  Graphical Representation of Histogram: 

A histogram (or rectangular diagram or block diagram) is a graphical representation of a frequency

distribution in the form of rectangles one after the other with height proportional to the frequencies.

It is two dimensional in which case the height as well as width of the rectangle matters.

Que:Represent the following data by means of a Histogram:

 Age( in years) 

20-

25

25-

30

30-

35

35-

40

40-

45

45-

50

50-

55

Number

of 

workers

3 4 5 6 5 4 3

3)  Frequency Polygon of a Line Graph: 

A frequency polygon can be constructed for a grouped frequency distribution, with equal-interval, in

two different ways:

Method I: 

  Represent the class-marks along the x-axis.   Represent the frequencies along y-axis. 

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   Join these points, in order, by straight lines.   The points at each end is joined to the immediate higher(or lower) class mark at zero frequency so

as to complete the polygon. 

Method II: 

  Represent a histogram of the given data. 

   Join the mid points of the tops of the adjacent rectangles by straight lines.   The mid points at each end are joined to the immediate higher (or lower) at zero frequency so asto complete the polygon. 

  The two classes, one at each end, are to be included. 

Construct a frequency polygon for the following data:

Monthly pocket expenses of a student  

0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40

Number of students 10 16 30 42 50 30 16 12

 Solution: Here we have

Monthly pocket expensesof a student(in $) 

class- marks  Number of students 

0-5 2.5 10

5-10 7.5 16

10-15 12.5 30

15-20 17.5 42

20-25 22.5 50

25-30 27.5 30

30-35 32.5 16

35-40 37.5 12

4)  Cumulative Frequency Curve(ogive): 

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Name: Shailesh Kumar Registration Number: 511035200 Semester: 3rd

Specialized Stream: Information Systems Management 

The Cumulative frequency curve for a grouped frequency distribution is obtained by plotting the points

and then joining them by a free-hand smooth curve.

This is also known as ogive.

Method: 

  Form the cumulative frequency table. 

  Mark the upper class limits along the x-axis.   Mark the cumulative frequencies along the y-axis.   Plot the points and join them by a free-hand smooth curve. 

Draw a cumulative frequency curve for the following data:

Marks 0-4 4-8 8-12 12-16 16-20

Number of students

4 6 10 8 4

The cumulative frequency table is as follows:

Marks  Number of students 

cumulative frequency  

0-4 4 4

4-8 6 4+6=10

8-12 10 10+10=20

12-16 8 20+8=28

16-20 4 28+4=32

Total 32

Joining these points by a free-hand smooth curve, we have the following cumulative frequency curve:

5)  Pie-chart or Pie-graph: 

It is drawn by first drawing a circle of a suitable radius and then dividing the angle of 360 degree at its

centre in proportion to the figures given under various heads.

Solution:

<AOB = 14 x 360 /100 = 50.4

<COD = 29 x 360 /100 = 104.4

<EOF = 16 x 360 /100 = 57.6

<BOC = 16 x 360 /100 = 57.6

<DOE = 17 x 360 /100 = 61.2

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Name: Shailesh Kumar Registration Number: 511035200 Semester: 3rd

Specialized Stream: Information Systems Management 

<FOA = 8 x 360 /100 = 28.8

Take a circle with centre O and unit radius.