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    MBA SEMESTER IIIMB0050 Research Methodology- 4 Credits(Book ID: B1206)Assignment Set- 1 (60 Marks)

    Q 1. Why should a manger know about research when the job entails managing people, products,events, environments, and the like?

    The manager, while managing people, products, events, and environments willinvariably faceproblems, big and small, and will have to seek ways to find longlasting effective solutions. Thiscan be achieved only through knowledge of research even if consultants are engaged to solveproblems.Basic research is important for generating and building upon the existing knowledge inthe areasof interest. It offers the foundation for applied research by which one can circumventreinventingthe wheel.Applied research is useful in solving specific problems in particularsituationswhere early action might be needed to solve problems in organizations.The managerwho knows how to relate to researchers facilitates the problemsolving process and benefits theresearch team as well as the organization. Theone who is not adept at this will frustrate and befrustrated during the researchprocess and thereafter.Being capable of handling the manager-researcher relationship is thus a bigadvantage and some of the nuances of handling research

    teams are:(i) knowing how much and what information to give to the team;(ii) meaningful andpurposeful interactions with the team members;2

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    Q 2. a. How do you evolve research design for exploratory research? Briefly analyze.

    Answer: a . Rese arc h de sign for exp l orat ory res ear ch:R e s e a r c h s i m p l y m e a n s a s e a r c h f o r f a c t s a n s w e r s t o q u e s t i o n sa n d s o l u t i o n s t o p ro b le ms . I t i s a p u rp o s i vei n v e s t i g a t i o n . I t i s a n o r g a n i z e d i n q u i r y . I t s e e k s t o f i n d ex plan ation s tou ne xp la ine d ph en ome non to cla rify the do ubt ful fa cts an d to co rre ctthemisconceived facts. Although any typology of research is inevitably arbitrary,Researchmay be classified crudely according to its major intent or the methods.It is al soknown as formulating research. It is preliminary study of anunfamil iar problemabout which the researcher has l i t t le or no knowledge. It is i l l -structured and much lessf o c u se d o n p re -d e t e r m i n e d o b j e c t i v e s . I t u s u a l l y t a k e s t h e f o r m o f a p i l o t s t u d y . T h e pu rpose of this research may be to generate new ideas, or to increase the researchers

    familiarity with the problem or to make a precise formulation of the problem or togatherinformation for clarifying concepts or to determine whether i t is feasible toattemptth es t u d y . K a t z c o n c e p t u a l i z e s t w o l e v e l s o f e x p l o r a t o r y s t u d i e s . A t t h e f i

    r s t l e v e l i s t h e d i s c o v e r y o f t h e s i g n i f i c a n t v a r i a b l e i n t h e s i t u a t i o n s ; a t t he second, the discovery of relationships between variables.

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

    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 hecould,he would have difficulty in understanding how these are inter-related. Therefore, herecords hisdecisions on paper or record disc by using relevant symbols or concepts. Such asymbolicconstruction may be called the research design or model. A research design is alogical andsystematic plan prepared for directing a research study.

    Dependent and Independent variables:A m ag n it ud e t ha t v ar ie s i s k no wn a s a v a ri ab le . T he c on ce pt m aya ss um e d i f fe re nt q u a n t i t a t i v e v a l u e s , l i k e h e i g h t , w e i g h t , i n c o m e , et c . Q u a l i t a t i v e v a r i a b l e s a r e n o t quantifiable in the strictest sense of objectivity.However, the qualitative phenomena mayals o be qu an t i f ied in te rms of thep resen ce o r absenc e o f t he a t t r i bu te cons i de red . Phenomena that assumedifferent values quantitatively even in decimal points are knownas continuous va ria bles .But, all variables need not be continuous. Values that can be

    expressed onl y in in teger values a re cal led non-cont inuous vari ab les.In statistical term,

    t h e y a re a l so kn o w n a s d is c re t e v a r i a b le . F o r ex a m p l e , ag e

    i s a c o n t i n u o u s v a r i a b l e ;

    w h e r e a s t h e n u m b e r o f c h i l d r e n i s a n o n - c o n t i n u o u s v a r i a b l e . W h e nc h a n ge s i n o ne v a r i a b l e d e p e n d s u p o n t h e c h a n g es i n o n eo r m o r e o t h e r v a r i a b l e s , i t i s k n o w n a s a d e p e n d e n t o r e n d o g e n o u s v a r i a ble , and the var iab les that cause the chan ges in the dependent variable areknown as the independent or explanatory or exogenous variables.For example, if deman ddepends upon price, then demand is a dependent variable, whi leprice is theindependent variable.And if, more variables determine demand, like income and prices ofsubstitute commodity, then demand also depends upon them in addition to the own

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    price. Then, demand isa d e p e n d e n t v a r i a b l e w h i c h i s d e t e r m i n e d b y t h e i n d e p e n d e n t v a r i a b l e s l i ke o wn p r i c e , income and price of substitute.Extraneous variable:The independent variables which are not directly related to the purpose of the studybut affect the dependent variable are known as extraneous variables. For instance,assume that a researcher wants to test the hypothesis that there is relationship betweenchildrens school performance and their self-concepts, in which case the latter is anindependent var iable and the former, the dependent var iable. In this context,int ell igence may also influence the school performance. However, since it is not directlyrelated to the purpose of the study undertaken by the researcher, it would be known as anextraneous variable. The influence caused by the extraneous variable on the dependent variableis technically called as an experimental error. Therefore, a research study should always beframed in such a manner that the dependent variable completely influences the change in the independentvariable and any other extraneous variable or variables.

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    Q 3. A. Differentiate between Census survey and Sample Survey.

    Census Survey Sample Survey

    A census measures absolutely everyone in the

    whole country. This obviously meansthat a census survey is a much bigger exercisein nature and procedures

    A part of the population is known as sample

    Census survey also is a very time consumingexercise as information needsto be collected from each and every individualfrom the population.

    On the other hand, sample survey iseasier as arepresentative sample is takenfrom the population and the results obtainedare extrapolated to fit the entire population.

    There are times and requirements wheregovernments have to indulge in census surveyeven if it is time consuming andvery expensive as it needs to formulatepolicies and welfare programs for thepopulation. For example, when a

    government has to count heads of thepopulation

    Sample surveys cannot count the numberof people in the country but whengovernment is planning on a welfareprogram for cancer patients, it can conduct a samplesurvey of some of thecancer patients and thenextrapolate

    theresults on the section of the populationthat isundergoing treatment for cancer.

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

    b. Analyze multi-stage and sequential sampling.

    Multi-stage sampling:In multi-stage sampling method, sampling is carried out in two or more stages. The populationisregarded as being composed of a number of second stage units and so forth. That is, ateachstage, a sampling unit is a cluster of the sampling units of the subsequent stage. First,asample of the first stage sampling units is drawn, then from each of the selected firststagesampling unit, a sample of the second stage sampling units is drawn. The procedure

    continuesdown to the final sampling units or population elements. Appropriate random samplingmethodis adopted at each stage. It is appropriate where the population is scattered over awidergeographical area and no frame or list is available for sampling. It is also useful when asurveyhas to be made within a limited time and cost budget. The major disadvantage is thattheprocedure of estimating sampling error and cost advantage is complicated.

    Sequential sampling:Sequential sampling is a non-probability sampling technique wherein the researcher picks asingle or a group of subjects in a given time interval, conducts his study, analyses the results thenpicks another group of subjects if needed and so on. This sampling technique gives theresearcher limitless chances of fine tuning his research methods and gaining a vital insight into thestudy that he is currently pursuing. There is very little effort in the part of the researcher whenperforming this sampling technique. It is not expensive, not time consuming and notworkforceextensive.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 samplesizesignificant enough to represent a big fraction of the entire population. Due to theaforementioned disadvantages, results from this sampling technique cannot be used to createconclusions andinterpretations pertaining to the entire population.

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    Q 4. List down various measures of central tendency and explain the difference between them?

    Answer:

    Measures of Central Tendency:The term central tendencyrefers to the "middle" value or perhaps a typical value of the data,and is measured using themean , median , or mode. Each of these measures is calculated differently, and the one that is best to use depends uponthe situation. Analysis of data involves understanding of the characteristics of the data. Thefollowing are the important characteristics of a statistical data:

    Central tendencyDispersionSkew ness

    Kurtosis In a data distribution, the individual items may have a tendency to come to a centralposition or an average value. For instance, in a mark distribution, the individual students mayscore 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 thecentral position of the distribution is called central tendency. Central tendency of the data ismeasured by statistical averages. Averages are classified into two groups.1. Mathematical averages2. Positional averages

    Statistical Averages

    Mathematical averages Positional averages

    Arithmetic mean MedianGeometric mean ModeHarmonic mean

    Arithmetic mean, geometric mean and harmonic mean are mathematical averages. Median andmode are positional averages. These statistical measures try to understand how individual valuesin a distribution concentrate to a central value like average. If the values of distributionapproximately come near to the average value, we conclude that the distribution has centraltendency.

    Difference between Mean and Median:

    Mean (Mathematical averages) Median (Positional averages)

    When the sample size is large and doesnot include outliers, the mean scoreusually provides a better measure of centraltendency.

    The median may be a better indicatorof the most typical value if a set of scoreshas anOutlier . An outlier is an extremevalue that differs greatly from othervalues.

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    The mean is the most commonly-usedmeasure of central tendency. When wetalk about an "average", we usually are referring tothe mean

    The median o ften i s used whenthere are a few ext reme valuesthat cou ld great ly i nf luence them e a n a n d d i s t o r t w h a t m i g h t b econsidered 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 valuesand taking the data point in the middle ofthe sequence

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    Q.5. Select any topic for research and explain how you will use both secondary and primarysources to gather the required information.

    Answer:For performing research on the literacy levels among families, the primary and secondarysources of data can be used very effectively. More specifically the primary sources of datacollection is suggested in this regard. Because personal data or data related to human beingsconsist of:

    1. Demographic and socio-economic characteristics of individuals: Age, sex, race, socialclass,religion, marital status, education, occupation income, family size, location of the householdlifestyle 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 relatedto geo-physical characteristics, resource endowment, population,occupational patterninfrastructure 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 ananalysis of factual data,no specific inferences canbe drawn on the questions under study. Inferences based onimagination or guess work cannot pr

    ovide correct answers to research questions. Therelevance, adequacy and reliability of datadetermine the quality of the findings of a study.Data form the basis for testing the hypothesisformulated in a study. Data also provide thefacts and figures required for constructingmeasurement scales and tables, which areanalyzedwith statistical techniques. Inferences on the results of statistical analysis and tests of significance provide the answers to research questions. Thus, the scientific process of measurements, analysis, testing and inferences depends on the availability of relevant dataand theiraccuracy. Hence, the importance of data for any research studiesThe sources of data may be classified into:a.Primary sourcesb.Secondary sources.Primary Sources of Data:Primary sources are original sources from which the researcher directly collects data thathavenot been previously collected e.g.., collection of data directly by the researcher on brandawa

    reness, brand preference, brand loyalty and other aspects of consumer behaviour from asampleof consumers by interviewing them,. Primary data are first-hand information collectedthroughvarious methods such as observation, interviewing, mailing etc.Advantage of Primary Data:It is original source of dataIt 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

    1. Demographic and socio-economic characteristics of individuals: Age, sex, race, socialclass,religion, marital status, education, occupation income, family size, location of the householdlifestyle 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 relatedto geo-physical characteristics, resource endowment, population,occupational patterninfrastructure 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 ananalysis of factual data,no specific inferences canbe drawn on the questions under study. Inferences based onimagination or guess work cannot provide correct answers to research questions. Therelevance, adequacy and reliability of datadetermine the quality of the findings of a study.Data form the basis for testing the hypothesisformulated in a study. Data also provide thefacts and figures required for constructingmeasurement scales and tables, which are

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    analyzedwith statistical techniques. Inferences on the results of statistical analysis and tests of significance provide the answers to research questions. Thus, the scientific process of measurements, analysis, testing and inferences depends on the availability of relevant dataand theiraccuracy. Hence, the importance of data for any research studiesThe sources of data may be classified into:a.Primary sourcesb.Secondary sources.Primary Sources of Data:Primary sources are original sources from which the researcher directly collects data thathavenot been previously collected e.g.., collection of data directly by the researcher on brandawareness, brand preference, brand loyalty and other aspects of consumer behaviour from asampleof consumers by interviewing them,. Primary data are first-hand information collectedthroughvarious methods such as observation, interviewing, mailing etc.Advantage of Primary Data:It is original source of dataIt 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 administerMethods of Collecting Primary Data:Primary data are directly collected by the researcher from their original sources. In this case,theresearcher can collect the required date precisely according to his research needs, he cancollectthem when he wants them and in the form he needs them. But the collection of primary data iscostly and time consuming. Yet, for several types of social science research requireddata are notavailable from secondary sources and they have to be directly gathered from theprimary sources.

    In such cases where the available data are in appropriate, inadequateorobsolete, primary data have to be gathered. They include: socioeconomic surveys, socialanthropological studies of rural communities and tribal communities, sociological studies of socialproblems and social institutions. Marketing research, leadership studies, opinion polls,attitudinalsurveys, readership, radio listening and T.V. viewing surveys, knowledge-awarenesspractice(KAP) studies, farm managements studies, business management studies etc. Thereare variousmethods of data collection. A Method is different from a Tool while a methodrefers to the way ormode of gathering data, a tool is an instruments used for the method. Forexample, a schedule isused 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 discussedin 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 anotherpurpose.

    The secondary sources consists of readily compendia and already compiled statisticalstatementsand reports whose data may be used by researchers for their studies e.g., censusreports , annualreports and financial statements of companies, Statistical statement, Reportsof GovernmentDepartments, Annual reports of currency and finance published by the ReserveBank of India,Statistical statements relating to Co-operatives and Regional Banks,publishedby the NABARD, Reports of the National sample survey Organization, Reports of tradeassociations, publications of international organizations such as UNO, IMF, World Bank,ILO,WHO, etc., Trade and Financial journals newspapers etc.Secondary sources consist of notonly published records and reports, but also unpublishedrecords. The latter category includesvarious records and registers maintained by the firms andorganizations, e.g., accounting and

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    financial records, personnel records, register of members,minutes of meetings, inventory recordsetc.Features of Secondary Sources:Though secondary sources are diverse and consist of all sorts of materials, theyhave certaincommon characteristics. First, they are readymade and readily available, and do notrequirethe trouble of constructing tools and administering themSecond, they consist of data whicha researcher has no original control over collectionandclassification. 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,secondarysources are not limited in time and space. That is, the researcher using them neednot have beenpresent when and where they were gathered

    Use of Secondary Data:The second data may be used in three ways by a researcher. First, some specificinformationfrom secondary sources may be used for reference purpose. For example, the generalstatistical information in the number of co-operative credit societies in the country, theircoverageof villages, their capital structure, volume of business etc., may be taken frompublished reports and quoted as background information in a study on the evaluation of performance of cooperativecredit societies in a selected district/state.

    Second, secondary data may be used as bench marks against which the findings ofresearchmaybe tested, e.g., the findings of a local or regional surveymay be compared with thenational averages; the performance indicators of a particular bankmay be tested against thecorresponding indicators of the banking industry as a whole; and soon.Finally, secondary data may be used as the sole source of information for a researchproject.Such studies as securities Market Behaviour, Financial Analysis of companies, Trade increditallocation in commercial banks, sociological studies on crimes, historical studies, and thelike,depend primarily on secondary data. Year books, statistical reports of governmentdepartments, report of public organizations of Bureau of Public Enterprises, Censes Reportsetc.,and serve as major data sources for such 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 documentsand reports are located, collection of data is just matter of desk work. Eventhe tediousness ofcopying the data from the source can now be avoided, thanks toXeroxing facilities.

    Wider geographical area and longer reference period may be covered without muchcost. Thus,the use of secondary data extends the researchers space and time reach.

    The use of secondary data broadens the data base from which scientific generalizationscan bemade.

    Environmental and cultural settings are required for the study.

    The use of secondary data enables a researcher to verify the findings bases on primarydata.It readily meets the need for additional empirical support. The researcher needsnot wait the timewhen additional primary data can be collected.Disadvantages of Secondary Data:The use of a secondary data has its own limitations.

    The most important limitation is the available data may not meet our specific needs.Thedefinitions adopted by those who collected those data may be different; units of measure maynot match; and time periods may also be different.

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    The available data may not be as accurate as desired. To assess their accuracy we needto knowhow the data were collected.

    The secondary data are not up-to-date and become obsolete when they appear inprint,because of time lag in producing them. For example, population census data arepublishedtwo or three years later after compilation and no new figures will be availablefor another tenyears.

    Finally, information about the whereabouts of sources may not be available to all socialscientists.Even if the location of the source is known, the accessibility depends primarilyon proximity. Forexample, 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 thembefore deciding to use them.1)

    Data Pertinence:

    The first consideration in evaluation is to examine the pertinence of the available secondary datato 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 therequirements of our research? On the basis of above consideration, the pertinence of thesecondary data to the research on hand should be determined, as a researcher who isimaginative and flexible may be able to redefine his research problem so as to make use ofotherwise unusable available data.2)

    Data Quality:If the researcher is convinced about the available secondary data for his needs, the next step isto examine the quality of the data. The quality of data refers to their accuracy, reliability andcompleteness. The assurance and reliability of the available secondary data depends on theorganization which collected them and the purpose for which they were collected. What is theauthority and prestige of the organization? Is it well recognized? Is it noted for reliability? It iscapable of collecting reliable data? Does it use trained and well qualified investigators? Theanswers to these questions determine the degree of confidence we can have in the data and theiraccuracy. It is important to go to the original source of the secondary data rather than to use animmediate source which has quoted from the original. Then only, the researcher can review thecautionary and other comments that were made in the original source.3)Data Completeness:

    The completeness refers to the actual coverage of the published data. This depends on themethodology and sampling design adopted by the original organization. Is the methodologysound? Is the sample size small or large? Is the sampling method appropriate? Answers to thesequestions may indicate the appropriateness and adequacy of the data for the problem understudy. The question of possible bias should also be examined. Whether the purpose for which theoriginal organization collected the data had a particular orientation? Has the study been made topromote the organizations own interest? How the study was conducted? These are importantclues. The researcher must be on guard when the source does not report the methodology andsampling design. Then it is not possible to determine the adequacy of the secondary data for theresearchers study.

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    Q 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 oftendesirableto use appropriate forms of graphic presentations. In additionsto tabular forms,graphic presentation involves use of graphics, charts and other pictorial devicessuch asdiagrams. These forms and devices reduce large masses of statistical data to a form thatcanbe quickly understood at the glance. The meaning of figures in tabular form may be difficultforthe mind to grasp or retain. Properly constructed graphs and charts relieve themind of burdensome details by portraying facts concisely, logically and simply. They, byemphasizingnew and significant relationship, are also useful in discovering new facts and indevelopinghypothesis. The device of graphic presentation is particularly useful when theprospective readers are non-technical people or general public. It is useful to even technicalpeople for dramatizing certainpoints about data; for important points can be more effectivelycaptured in pictures than intables. However, graphic forms are not substitutes for tables, but are

    additional tools for theresearcher to emphasize the research findings. Graphic presentation mustbe planned with utmost care and diligence. Graphic forms usedshould be simple, clear andaccurate and also be appropriate to the data. In planning this work,the following questions mustbe 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 hardnessof 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 adiverserange of areas. Increasingly sophisticated visual representations are emerging and, toenableeffective communication, insight is required into how diagrams are used and when theyareappropriate for use. The pervasive, everyday use of diagrams for communicatinginformationand ideas serves to illustrate the importance of providing a sound understanding of therolethat diagrams can, and do, play. Research in the field of diagrams aims toimprove ourunderstanding of the role of diagrams, sketches and other visualizations incommunication,computation, cognition, creative thought, and problem solving. These concerns

    have triggereda surge of interest in the study of diagrams.The study of diagrammaticcommunication as a whole must be pursued as an interdisciplinaryendeavor. Diagrams attracta large number of researchers from virtually all related fields,placing the conference as a majorinternational 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 statisticalanalysis. 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

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    impression on the mind and make intelligible and easily understandable the salient features of thedata. Forecasting also becomes easier with the help of graph. Thus it is of interest to study thegraphical representation of data. The graphical representation of data is categorized as basic fivetypes:

    1)Bar graph2)Pie graph3)Line graph4)Scatter plot5)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 (rectanglesof samewidth).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

    2) Graphical Representation of Histogram:A histogram (or rectangular diagram or block diagram) is a graphical representation of afrequency distribution in the form of rectangles one after the other with height proportional to thefrequencies.

    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:

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    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.

    Join these points, in order, by straight lines.

    The points at each end is joined to the immediate higher(or lower) class mark at zerofrequency 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 zerofrequency so asto complete the polygon.

    The two classes, one at each end, are to be included.Construct a frequency polygon for the following data:

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    4)Cumulative Frequency Curve(ogive):

    The Cumulative frequency curve for a grouped frequency distribution is obtained by plottingthepoints and then joining them by a free-hand smooth curve.This is also known asogive.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:

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    MBA SEMESTER IIIMB0034 Research Methodology- 4 Credits(Book ID: B1206)Assignment Set- 2

    Q 1. What is questionnaire? Discuss the main points that you will take into account while draftinga questionnaire?