Master of Business Administration

Semester III

MB0050- Research Methodology

Assignment

Set- 1

Q.1 a. Distinguish between Doubles sampling and multiphase sampling. b. What is replicated or interpenetrating sampling?

Answer:

a. Distinguish between Doubles sampling and multiphase sampling.

A standard form of sample design for industrial inspection purposes. In accordance with the characteristics of a particular plan, two samples are drawn, n1 and n2, and the first sample inspected. The batch can then be accepted or rejected upon the results of this inspection or the second sample be inspected and the decision made upon the combined result.

Double sampling plans were invented to give a questionable lot another chance.

For example, if in double sampling the results of the first sample are not conclusive with regard to accepting or rejecting, a second sample is taken. Application of double sampling requires that a first sample of size n1 is taken at random from the (large) lot. The number of defectives is then counted and compared to the first sample's acceptance number a1 and rejection number r1.

Denote the number of defectives in sample 1 by d1 and in sample 2 by d2, then:

If d1   a1, the lot is accepted. 

If d1   r1, the lot is rejected.If a1 < d1 < r1, a second sample is taken.If a second sample of size n2 is taken, the number of defectives, d2, is counted. The total number of defectives is D2 = d1 + d2. Now this is compared to the acceptance number a2 and the rejection number r2 of sample 2. In double sampling, r2 = a2 + 1 to ensure a decision on the sample.

If D2   a2, the lot is accepted. If D2   r2, the lot is rejected.

MULTI-PHASE SAMPLING

Definition:

It is sometimes convenient and economical to collect certain items of information from the whole of the units of a sample and other items of usually more detailed information from a sub-sample of the units constituting the original sample. This may be termed two-phase sampling, e.g. if the collection of information concerning variate, y, is relatively expensive, and there exists some other variate, x, correlated with it, which is relatively cheap to investigate, it may be profitable to carry out sampling in two phases.

At the first phase, x is investigated, and the information thus obtained is used either (a) to stratify the population at the second phase, when y is investigated, or (b) as supplementary information at the second phase, a ratio or regression estimate being used.

Two-phase sampling is sometimes called "double sampling".

Multistage sampling is a complex form of cluster sampling.

Advantages

cost and speed that the survey can be done in

convenience of finding the survey sample

normally more accurate than cluster sampling for the same size sample

Disadvantages

Is not as accurate as SRS if the sample is the same size

More testing is difficult to do

Using all the sample elements in all the selected clusters may be prohibitively expensive or not necessary. Under these circumstances, multistage cluster sampling becomes useful. Instead of using all the elements contained in the selected clusters, the researcher randomly selects elements from each cluster. Constructing the clusters is the first stage. Deciding what elements within the cluster to use is the second stage. The technique is used frequently when a complete list of all members of the population does not exist and is inappropriate.

b. What is replicated or interpenetrating sampling?

Replication is not the same as repeated measurements of the same item: they are dealt with differently in statistical experimental design and data analysis.

For proper sampling, a process or batch of products should be in reasonable statistical control; inherent random variation is present but variation due to assignable (special) causes is not. Evaluation or testing of a single item does not allow for item-to-item variation and may not represent the batch or process. Replication is needed to account for this variation among items and treatments.

Example: As an example, consider a continuous process which produces items. Batches of items are then processed or treated. Finally, tests or measurements are conducted. Several options might be available to obtain ten test values. Some possibilities are:

One finished and treated item might be measured repeatedly to obtain ten test results. Only one item was measured so there is no replication. The repeated measurements help identify observational error.

Ten finished and treated items might be taken from a batch and each measured once. This is not full replication because the ten samples neither are not random and not representative of the continuous nor batch processing.

Five items are taken from the continuous process based on sound statistical sampling. These are processed in a batch and tested twice each. This includes replication of initial samples but does not allow for batch-to-batch variation in processing. The repeated tests on each provide some measure and control of testing error.

Five items are taken from the continuous process based on sound statistical sampling. These are processed in five different batches and tested twice each. This plan includes proper replication of initial samples and also includes batch-to-batch variation. The repeated tests on each provide some measure and control of testing error.

Each option would call for different data analysis methods and yield different conclusions.

2. What are the differences between observation and interviewing as methods of data collection?

Give two specific examples of situations where either observation or interviewing would be more.

Answer:

Observation means viewing or seeing.

Observation may be defined as a systematic viewing of a specific phenomenon in its proper setting for the specific purpose of gathering data for a particular study. Observation is classical method of scientific study.

Observation as a method of data collection has certain characteristics .

1. It is both a physical and a mental activity:

The observing eye catches many things that are present. But attention is focused on data that are pertinent to the given study.

2. Observation is selective:

A researcher does not observe anything and everything, but selects the range of things to be observed on the basis of the nature, scope and objectives of his study. For example, suppose a researcher desires to study the causes of city road accidents and also formulated a tentative hypothesis that accidents are caused by violation of traffic rules and over speeding. When he observed the movements of vehicles on the road, many things are before his eyes; the type, make, size and colour of the vehicles, the persons sitting in them, their hair style, etc. All such things which are not relevant to his study are ignored and only over speeding and traffic violations are keenly observed by him.

3. Observation is purposive and not casual:

It is made for the specific purpose of noting things relevant to the study. It captures the natural social context in which persons behaviour occur. It grasps the significant events and occurrences that affect social relations of the participants.

4. Observation should be exact and be based on standardized tools of research and such as observation schedule, social metric scale etc., and precision instruments, if any.

Interviewing is one of the prominent methods of data collection .

It may be defined as a two way systematic conversation between an investigator and an informant, initiated for obtaining information relevant to a specific study. It involves not only conversation, but also learning from the respondent’s gesture, facial expressions and pauses, and his environment. Interviewing requires face to face contact or contact over telephone and calls for interviewing skills. It is done by using a structured schedule or an unstructured guide.

Interviewing may be used either as a main method or as a supplementary one in studies of persons. Interviewing is the only suitable method for gathering information from illiterate or less educated respondents. It is useful for collecting a wide range of data from factual demographic data to highly personal and intimate information relating to a person’s opinions, attitudes, values, beliefs past experience and future intentions. When qualitative information is required or probing is necessary to draw out fully, and then interviewing is required. Where the area covered for the survey is a compact, or when a sufficient number of qualified interviewers are available, personal interview is feasible.

Interview is often superior to other data-gathering methods. People are usually more willing to talk than to write. Once report is established, even confidential information may be obtained. It permits probing into the context and reasons for answers to questions.

Interview can add flesh to statistical information. It enables the investigator to grasp the behavioural context of the data furnished by the respondents.

Observation is suitable for a variety of research purposes. It may be used for studying

(a) The behavior of human beings in purchasing goods and services: life style, customs, and manner, interpersonal relations, group dynamics, crowd behavior, leadership styles, managerial style, other behaviours and actions;

(b) The behaviour of other living creatures like birds, animals etc.

(c) Physical characteristics of inanimate things like stores, factories, residences etc.

(d) Flow of traffic and parking problems.

(e) Movement of materials and products through a plant.

3. How is the Case Study method useful in Business Research?

Answer:

Case Study as a Method of Business Research

In-depth analysis of selected cases is of particular value to business research when a complex set of variables may be at work in generating observed results and intensive study is needed to unravel the complexities. For instance, an in-depth study of a firm’s top sales people and comparison with the worst sales people might reveal characteristics common to stellar performers. The exploratory investigator is best served by the active curiosity and willingness to deviate from the initial plan, when the finding suggests new courses of enquiry, might prove more productive

Case study of particular value when a complex set of variables may be at work in generating observed results and intensive study is needed to unravel the complexities. For example, an in-depth study of a firm’s top sales people and comparison with worst salespeople might reveal characteristics common to stellar performers. Here again, the exploratory investigation is best served by an active curiosity and willingness to deviate from the initial plan when findings suggest new courses of inquiry might prove more productive. It is easy to see how the exploratory research objectives of generating insights and hypothesis would be well served by use of this technique.

Making Case Study Effective

John Dollard has proposed seven criteria for evaluating such adequacy as follows:

i) The subject must be viewed as a specimen in a cultural series. That is, the case drawn out from its total context for the purposes of study must be considered a member of the particular cultural group or community. The scrutiny of the life histories of persons must be done with a view to identify the community values, standards and their shared way of life.

ii) The organic motto of action must be socially relevant. That is, the action of the individual cases must be viewed as a series of reactions to social stimuli or situation. In other words, the social meaning of behaviour must be taken into consideration.

iii) The strategic role of the family group in transmitting the culture must be recognized. That is, in case of an individual being the member of a family, the role of family in shaping his behaviour must never be overlooked.

iv) The specific method of elaboration of organic material onto social behaviour must be clearly shown. That is case histories that portray in detail how basically a biological organism, the man, gradually blossoms forth into a social person, are especially fruitful.

v) The continuous related character of experience for childhood through adulthood must be stressed. In other words, the life history must be a configuration depicting the inter-relationships between the people’s various experiences.

vi) Social situation must be carefully and continuously specified as a factor. One of the important criteria for the life history is that a person’s life must be shown as unfolding itself in the context of and partly owing to specific social situations.

vii) The life history material itself must be organized according to some conceptual framework; this in turn would facilitate generalizations at a higher level

4. Would case studies be considered as scientific research? Why or why not?

Answer:

Case Studies

 Case studies are a tool for discussing scientific integrity. Although one of the most frequently used tools for encouraging discussion, cases are only one of many possible tools. Many of the principles discussed below for discussing case studies can be generalized to other approaches to encouraging discussion about research ethics.

Cases are designed to confront readers with specific real-life problems that do not lend themselves to easy answers. Case discussion demands critical and analytical skills and, when implemented in small groups, also fosters collaboration (Pimple, 2002). By providing a focus for discussion, cases help trainees to define or refine their own standards, to appreciate alternative approaches to identifying and resolving ethical problems, and to develop skills for analyzing and dealing with hard problems on their own.

The effective use of case studies is comprised of many factors, including: appropriate selection of case(s) (topic, relevance, length, complexity)method of case presentation (verbal, printed, before or during discussion)format for case discussion (Email or Internet-based, small group, large group)leadership of case discussion (choice of discussion leader, roles and responsibilities for discussion leader)outcomes for case discussion (answers to specific questions, answers to general questions, written or verbal summaries)

Research methods don't seem so intimidating when you're familiar with the terminology. This is important whether you're conducting evaluation or merely reading articles about other studies to incorporate in your program. To help with understanding, here are some basic definitions used.

Variable:

Characteristics by which people or things can be described. Must have more than one level; in other words, to be able to change over time for the same person/object, or from person to person, or object to object. Some variables, called attributes, cannot be manipulated by the researcher (e.g., socioeconomic status, IQ score, race, gender, etc.). Some variables can be manipulated but are not in a particular study. This occurs when subjects self-select the level of the independent variable, or the level is naturally occurring (as with ex post facto research).

Manipulation:

Random assignment of subjects to levels of the independent variable (treatment groups).

Independent variable:

The treatment, factor, or presumed cause that will produce a change in the dependent variable. This is what the experimenter tries to manipulate. It is denoted as "X" on the horizontal axis of a graph.

Dependent variable:

The presumed effect or consequence resulting from changes in the independent variable. This is the observation made and is denoted by "Y" on the vertical axis of a graph. The score of "Y" depends on the score of "X."

Population:

The complete set of subjects that can be studied: people, objects, animals, plants, etc.

Sample:

A subset of subjects that can be studied to make the research project more manageable.

There are varieties of ways samples can be taken. If a large enough random samples are taken, the results can be statistically similar to taking a census of an entire population--with reduced effort and cost.

Case Study: A case study is conducted for similar purpose as the above but is usually done with a smaller sample size for more in-depth study. A case study often involves direct observation or interviews with single subjects or single small social units such as a family, club, school classroom, etc.

This is typically considered qualitative research.

Purpose: Explain or Predict Type of Research to Use: Relational Study

 In a relational study you start with a research hypothesis, that is, is what you're trying to "prove."

Examples of research hypotheses for a relational study: The older the person, the more health problems he or she encounters.

5. What are the contents of research reports?

Answer:

The outline of a research report is given below:

I. Prefatory Items

Title page

Declaration

Certificates

Preface/acknowledgements

Table of contents· List of tables

List of graphs/figures/charts

Abstract or synopsis

II. Body of the Report

Introduction

Theoretical background of the topic

Statement of the problem

Review of literature· The scope of the study

The objectives of the study

Hypothesis to be tested

Definition of the concepts

Models if any

Design of the study Methodology

Method of data collection

Sources of data

Sampling plan

Data collection instruments

Field work

Data processing and analysis plan

Overview of the report

Limitation of the study

Results: findings and discussions

Summary, conclusions and recommendations

III. Reference Material

Bibliography

Appendix

Copies of data collection instruments

Technical details on sampling plan

Complex tables

Glossary of new terms used.

6. Write short notes on the following:

a. Medianb. Standard Deviation

Answer:

a. Median

One problem with using the mean is that it often does not depict the typical outcome. If there is one outcome that is very far from the rest of the data, then the mean will be strongly affected by this outcome. Such an outcome is called and outlier. An alternative measure is the median. The median is the middle score. If we have an even number of events we take the average of the two middles. The median is better for describing the typical value. It is often used for income and home prices.

Example:

Suppose you randomly selected 10 house prices in the South Lake Tahoe area.  You are interested in the typical house price.  In $100,000 the prices were

        2.7,   2.9,   3.1,   3.4,   3.7, 4.1,   4.3,   4.7, 4.7, 40.8

If we computed the mean, we would say that the average house price is 744,000.  Although this number is true, it does not reflect the price for available housing in South Lake Tahoe.  A closer look at the data shows that the house valued at 40.8 x $100,000 = $4.08 million skews the data.  Instead, we use the median.  Since there is an even number of outcomes, we take the average of the middle two

      3.7 + 4.1                        = 3.9            2

The median house price is $390,000.  This better reflects what house shoppers should expect to spend.

There is an alternative value that also is resistant to outliers.  This is called the trimmed mean which is the mean after getting rid of the outliers or 5% on the top and5% on the bottom. We can also use the trimmed mean if we are concerned with outliers skewing the data; however the median is used more often since more people understand it.

Example:

At a ski rental shop data was collected on the number of rentals on each of ten consecutive Saturdays: 

        44, 50, 38, 96, 42, 47, 40, 39, 46, 50.

 

To find the sample mean, add them and divide by 10:

         44 + 50 + 38 + 96 + 42 + 47 + 40 + 39 + 46 + 50                                                                                        = 49.2                                        10

Notice that the mean value is not a value of the sample.

To find the median, first sort the data:

        38, 39, 40, 42, 44, 46, 47, 50, 50, 96

Notice that there are two middle numbers 44 and 46.  To find the median we take the average of the two.

                             44 + 46        Median =                      = 45                                  2

Notice also that the mean is larger than all but three of the data points.  The mean is influenced by outliers while the median is robust.

b. Standard Deviation

Standard Deviation

The mean, mode, median, and trimmed mean do a nice job in telling where the center of the data set is, but often we are interested in more. 

For example, a pharmaceutical engineer develops a new drug that regulates iron in the blood.  Suppose she finds out that the average sugar content after taking the medication is the optimal level.  This does not mean that the drug is effective.  There is a possibility that half of the patients have dangerously low sugar content while the other half has dangerously high content.  Instead of the drug being an effective regulator, it is a deadly poison.  What the pharmacist needs is a measure of how far the data is spread apart.  This is what the variance and standard deviation do.  First we show the formulas for these measurements.  Then we will go through the steps on how to use the formulas.

We define the variance to be 

        

and the standard deviation to be

        

Variance and Standard Deviation:

Step by Step

1. Calculate the mean, x. 2. Write a table that subtracts the mean from each observed value.3. Square each of the differences.4. Add this column.5. Divide by n -1 where n is the number of items in the sample. This is the variance.6. To get the standard deviation we take the square root of the variance.  

Example:

The owner of the Ches Tahoe restaurant is interested in how much people spend at the restaurant.  He examines 10 randomly selected receipts for parties of four and writes down the following data.

        44,   50,   38,   96,   42,   47,   40,   39,   46,   50

He calculated the mean by adding and dividing by 10 to get

        x = 49.2

Below is the table for getting the standard deviation:

x x - 49.2 (x - 49.2 )2

44 -5.2 27.04

50 0.8 0.64

38 11.2 125.44

96 46.8 2190.24

42 -7.2 51.84

47 -2.2 4.84

40 -9.2 84.64

39 -10.2 104.04

46 -3.2 10.24

50 0.8 0.64

Total 2600.4

Now 

        2600.4                         = 288.7        10 - 1

Hence the variance is 289 and the standard deviation is the square root of 289 = 17.

Since the standard deviation can be thought of measuring how far the data values lie from the mean, we take the mean and move one standard deviation in either direction.  The mean for this example was about 49.2 and the standard deviation was 17.  We have: 49.2 - 17 = 32.2

 and 49.2 + 17 = 66.2 What this means is that most of the patrons probably spent between $32.20 and $66.20.

The sample standard deviation will be denoted by s and the population standard deviation will be denoted by the Greek letter.

The sample variance will be denoted by s2 and the population variance will be denoted by 2.

The variance and standard deviation describe how spread out the data is. If the data all lies close to the mean, then the standard deviation will be small, while if the data is spread out over a large range of values, s will be large.  Having outliers will increase the standard deviation.

One of the flaws involved with the standard deviation, is that it depends on the units that are used.  One way of handling this difficulty, is called the coefficient of variation which is the standard deviation divided by the mean times 100%

                                  CV =           100%                                

In the above example, it is 

         17                   100%   = 34.6%        49.2

This tells us that the standard deviation of the restaurant bills is 34.6% of the mean.

Set - 2

1. What is the significance of research in social and business sciences?

Answer:

Significance of Research in Social and Business Sciences

According to a famous Hudson Maxim, “All progress is born of inquiry. Doubt is often better than overconfidence, for it leads to inquiry, and inquiry leads to invention”. It brings out the significance of research, increased amounts of which makes progress possible. Research encourages scientific and inductive thinking, besides promoting the development of logical habits of thinking and organization.

The role of research in applied economics in the context of an economy or business is greatly increasing in modern times. The increasingly complex nature of government and business has raised the use of research in solving operational problems. Research assumes significant role in formulation of economic policy, for both the government and business. It provides the basis for almost all government policies of an economic system. Government budget formulation, for example, depends particularly on the analysis of needs and desires of the people, and the availability of revenues, which requires research. Research helps to formulate alternative policies, in addition to examining the consequences of these alternatives. Thus, research also facilitates the decision making of policy-makers, although in itself it is not a part of research. In the process, research also helps in the proper allocation of a country’s scare resources. Research is also necessary for collecting information on the social and economic structure of an economy to understand the process of change occurring in the country. Collection of statistical information though not a routine task, involves various research problems.

Therefore, large staff of research technicians or experts is engaged by the government these days to undertake this work.

Thus, research as a tool of government economic policy formulation involves three distinct stages of operation which are as follows:

Investigation of economic structure through continual compilation of facts

Diagnoses of events that are taking place and the analysis of the forces underlying them;

and

The prognosis, i.e., the prediction of future developments

Research also assumes a significant role in solving various operational and planning problems associated with business and industry. In several ways, operations research, market research, and motivational research are vital and their results assist in taking business decisions. Market research is refers to the investigation of the structure and development of a market for the formulation of efficient policies relating to purchases, production and sales. Operational research relates to the application of logical, mathematical, and analytical techniques to find solution to

business problems such as cost minimization or profit maximization, or the optimization problems. Motivational research helps to determine why people behave in the manner they do with respect to market characteristics.

More specifically, it is concerned with the analyzing the motivations underlying consumer behaviour. All these researches are very useful for business and industry, which are responsible for business decision making.

Research is equally important to social scientist for analyzing social relationships and seeking explanations to various social problems. It gives intellectual satisfaction of knowing things for the sake of knowledge. It also possesses practical utility for the social scientist to gain knowledge so as to be able to do something better or in a more efficient manner. This, research in social sciences is concerned with both knowledge for its own sake, and knowledge for what it can contribute to solve practical problems.

2. What is the meaning of hypothesis? Discuss the types of hypothesis.

Answer:

Meaning of hypothesis:

The relationship between/ among variables,

The research hypothesis is a predictive statement, capable for being tested by scientific methods, that relates an independent variable to some dependent variable. The level of influence of independent variables on the dependent variables.

E.g.: “students who receive counseling will show a greater increase in creativity than students not receiving counseling.”

A proposal intended to explain certain facts or observations.

A hypothesis is a precise testable statement prediction of what the researcher expects to find or prove.

It is a tentative answer to a research question.

A hypothesis is a tentative proposition formulated for empirical testing. It is a declarative statement combining concept.

Definition of hypothesis:

Goode and Hatt have defined a hypothesis, “a proposition which can be put to test to determine validity.”

Various types of Hypothesis:

1. Descriptive hypothesis:

These are propositions that describe the characteristics (such as size, form, or distribution) of a variable. The variable may be an object, person, organization, situation or event.

Some examples are:

“The rate of unemployment among arts graduates is higher than that of commerce graduates.”“Public enterprises are more amenable for centralized planning.”

2. Relational hypothesis:

These are propositions, which describe the relationship between two variables. T h e relationship suggested may be positive or negative correlation or causal relationship.

Some examples:

“Families with higher incomes spend more for recreation.”“The lower the rate of job turnover in a work group, the higher the work  productivity.”

3. Casual hypothesis:

State that the existence of, or a change in, one variable causes or leads to an effect on another variables. The first variable is called the independent variable, and the latter the dependent variables the researcher must consider the direction in which such relationships flow.ie. Which are cause and which effect is

4. Working hypothesis:

While planning the study of a problem, hypotheses are formed. Initially they are not be very specific. In such cases, they are referred to as “Working hypothesis “which are subject to modification as the investigation proceeds.

5. Null hypothesis:

These are hypothetical statements denying what are explicitly indicated in working hypothesis. They are formed in the negative statement.

For example:

” There is no relationship between families’ income level a n d expenditure on recreation”.

Null hypothesis are formulated for testing statistical significance. Since, this form is a convenient approach to statistical analysis. As the test would nullify the null hypothesis, they are so called. There is some justification for using null hypotheses. They conform to the qualities of detachment and objectivity to be possessed by are searcher. If the attempts to test hypotheses which he assumes to be true, it would appear as if he is not behaving objectively.The problem does not arise when he uses null hypotheses. Moreover, null hypotheses are more exact. It is easier to reject the contrary of hypotheses than to confirm it with complete certainty. Hence the concept of null hypothesis is found to be very useful.

6. Alternate Hypothesis {Ha}

It is a statement, which is accepted, after a null hypothesis is rejected based on the test result.Ex: If the null hypothesis is that “there is no relationship between the eye colour of husbands and wives”, it is rejected then automatically the alternative hypothesis is that “there is relationship between the eye colour of husbands and wives is accepted.”

7. Statistical hypothesis:

There are statements about a statistical population. These are derived from a sample. These are quantitative in nature in that they are numerically measurable, e.g., “Group A is older than Group B.”

8. Common sense Hypothesis:

These represent the common sense ideas. They state the existence of empirical uniformities perceived through day-to-day observations.“Soldiers from upper-class are less adjusted in the army than lower class men”“Fresh students conform to the conventions set up by seniors”

9. Complex Hypothesis:

These aim at testing the existence of logically derived relationships between empirical uniformities.

For example, “The concentric growth circles characterize a city”.

10. Analytical Hypothesis:

These are concerned with the relationship of analytic variables. These hypotheses occur at the highest level of abstraction. These specify relationship between changes in one property and changes in another.

3) What is frequency distribution? What are the types and general rules for graphical representation of data?

Answer:

Frequency Distribution

Frequency Distribution: Variables that are classified according to magnitude or size are often arranged in the form of a frequency table. In constructing this table, it is necessary to determine the number of class intervals to be used and the size of the class intervals. A distinction is usually made between continuous and discrete variables. A continuous variable has an unlimited number of possible values between the lowest and highest with no gaps or breaks. Examples of continuous variable are age, weight, temperature etc. A discrete variable can have a series of specified values with no possibility of values between these points. Each value of a discrete variable is distinct and separate.

Types of Graphs and General Rules

The most commonly used graphic forms may be grouped into the following categories:

a) Line Graphs or Charts

b) Bar Charts

c) Segmental presentations.

d) Scatter plots

e) Bubble charts

f) Stock plots

g) Pictographs

h) Chesnokov Faces

The general rules to be followed in graphic representations are:

1. The chart should have a title placed directly above the chart.

2. The title should be clear, concise and simple and should describe the nature of the data

presented.

3. Numerical data upon which the chart is based should be presented in an accompanying table.

4. The horizontal line measures time or independent variable and the vertical line the measured

variable.

5. Measurements proceed from left to right on the horizontal line and from bottom to top on the

vertical.

6. Each curve or bar on the chart should be labelled.

7. If there are more than one curves or bar, they should be clearly differentiated from one another

by distinct patterns or colours.

8. The zero point should always be represented and the scale intervals should be equal.

9. Graphic forms should be used sparingly. Too many forms detract rather than illuminating the

presentation.

10. Graphic forms should follow and not precede the related textual discussion.

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

Answer:

Central tendency

Central tendency: central tendency relates to the way in which quantitative data is clustered around some value. A measure of central tendency is a way of specifying - central value. In practical statistical analysis, the terms are often used before one has chosen even a preliminary form of analysis: thus an initial objective might be to "choose an appropriate measure of central tendency".

In the simplest cases, the measure of central tendency is an average of a set of measurements, the word average being variously construed as mean, median, or other measure of location, depending on the context. However, the term is applied to multidimensional data as well as to univariate data and in situations where a transformation of the data values for some or all dimensions would usually be considered necessary: in the latter cases, the notion of a "central location" is retained in converting an "average" computed for the transformed data back to the original units. In addition, there are several different kinds of calculations for central tendency, where the kind of calculation depends on the type of data (level of measurement).

Both "central tendency" and "measure of central tendency" apply to either statistical populations or to samples from a population.

Basic measures of central tendency

The following may be applied to individual dimensions of multidimensional data, after transformation, although some of these involve their own implicit transformation of the data.

Arithmetic mean - the sum of all measurements divided by the number of observations in the data set

Median - the middle value that separates the higher half from the lower half of the data set

Mode - the most frequent value in the data set Geometric mean - the n th root of the product of the data values Harmonic mean - the reciprocal of the arithmetic mean of the reciprocals of the data

values Weighted mean - an arithmetic mean that incorporates weighting to certain data elements Truncated mean - the arithmetic mean of data values after a certain number or proportion

of the highest and lowers data values have been discarded. Midrange - the arithmetic mean of the maximum and minimum values of a data set.

Arithmetic mean:

In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space.

The term "arithmetic mean" is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent. For example, per capita GDP gives an approximation of the arithmetic average income of a nation's population.

While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers. Notably, for skewed distributions, the arithmetic mean may not accord with one's notion of "middle", and robust statistics such as the median may be a better description of central tendency.

Median:

A median is described as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.

In a sample of data, or a finite population, there may be no member of the sample whose value is identical to the median (in the case of an even sample size), and, if there is such a member, there may be more than one so that the median may not uniquely identify a sample member. Nonetheless, the value of the median is uniquely determined with the usual definition. A related concept, in which the outcome is forced to correspond to a member of the sample, is the medoid.

At most, half the population have values less than the median, and, at most, half have values greater than the median. If both groups contain less than half the population, then some of the population is exactly equal to the median. For example, if a < b < c, then the median of the list {a, b, c} is b, and, if a < b < c < d, then the median of the list {a, b, c, d} is the mean of b and c; i.e., it is (b + c)/2.

The median can be used as a measure of location when a distribution is skewed, when end-values are not known, or when one requires reduced importance to be attached to outliers, e.g., because they may be measurement errors. A disadvantage of the median is the difficulty of handling it theoretically.

Mode (statistics):

In statistics, the mode is the value that occurs most frequently in a data set or a probability distribution. In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score.

Like the statistical mean and the median, the mode is a way of capturing important information about a random variable or a population in a single quantity. The mode is in general different from the mean and median, and may be very different for strongly skewed distributions.

The mode is not necessarily unique, since the same maximum frequency may be attained at different values. The most ambiguous case occurs in uniform distributions, wherein all values are equally likely.

Geometric mean:

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, except that the numbers are multiplied and then the n th root (where n is the count of numbers in the set) of the resulting product is taken.

For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is 2√ 2 × 8 = 4. As another example, the geometric mean of the three numbers 4, 1,

and 1/32 is the cube root of their product (1/8), which is 1/2; that is 3√ 4 × 1 × 1/32 = ½ .

The geometric mean can also be understood in terms of geometry. The geometric mean of two numbers, a and b, is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a and b. Similarly, the geometric mean of three numbers, a, b, and c, is the length of one side of a cube whose volume is the same as that of a right cuboid with sides whose lengths are equal to the three given numbers.

The geometric mean only applies to positive numbers.[1] It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.

The geometric mean is also one of the three classic Pythagorean means, together with the aforementioned arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between (see Inequality of arithmetic and geometric means.)

Harmonic mean:

The harmonic mean (sometimes called the sub contrary mean) is one of several kinds of average. Typically, it is appropriate for situations when the average of rates is desired.

The harmonic mean H of the positive real numbers x1, x2, ..., xn > 0 is defined to be

From the third formula in the above equation it is more apparent that the harmonic mean is related to the arithmetic and geometric means.

Equivalently, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. As a

simple example, the harmonic mean of 1, 2, and 4 is

Weighted mean:

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counter-intuitive properties, as captured for instance in Simpson's paradox.

The term weighted average usually refers to a weighted arithmetic mean, but weighted versions of other means can also be calculated, such as the weighted geometric mean and the weighted

Truncated mean:

A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both.

For most statistical applications, 5 to 25 percent of the ends are discarded. In some regions of Central Europe it is also known as a Windsor mean, but this name should not be confused with the Winsorized mean: in the latter, the observations that the trimmed mean would discard are instead replaced by the largest/smallest of the remaining values.

Mid-range:

The mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, or:

As such it is a measure of central tendency.

The midrange is highly sensitive to outliers and ignores all but two data points. It is therefore a very non-robust statistic (having a breakdown point of 0, meaning that a single observation can change it arbitrarily), and it is rarely used in statistical analysis.

The midhinge is the 25% trimmed mid-range, and is more robust, having a breakdown point of 25%.

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 answers to 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 and (b) secondary sources.

Primary Sources of Data

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 behavior from a sample 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 inappropriate, inadequate or obsolete, primary data have to be gathered. They include: socio economic 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, business management 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 the method.

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.

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 and classification. 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 selected district/state.

Second, secondary data may be used as bench marks against which the findings of research may be 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, 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 documents and reports are located, collection of data is just matter of desk work. Even the 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 need not wait the time when 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. 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.

6. Write short notes on the following:

a. Dispersion b. Mathematical averages

Answer:

DispersionA modern student of statistics is mainly interested in the study of variability and uncertainty. In this section we shall discuss variability and its measures and uncertainty will be discussed in probability.

We live in a changing world. Changes are taking place in every sphere of life. A man of statistics does not show much interest in those things which are constant. The total area of the earth may not be very important to a research minded person but the area under different crops, area covered by forests, area covered by residential and commercial buildings are figures of great importance because these figures keep on changing form time to time and from place to place. Very large number of experts is engaged in the study of changing phenomenon. Experts working in different countries of the world keep a watch on forces which are responsible for bringing changes in the fields of human interest. The agricultural, industrial and mineral production and their transportation from one part to the other parts of the world are the matters of great interest to the economists, statisticians, and other experts. The changes in human population, the changes in standard living, and changes in literacy rate and the changes in price attract the experts to make detailed studies about them and then correlate these changes with the human life.

Thus variability or variation is something connected with human life and study is very important for mankind.

Dispersion:

The word dispersion has a technical meaning in statistics. The average measures the center of the data. It is one aspect observations. Another feature of the observations is as to how the observations are spread about the center. The observation may be close to the center or they may be spread away from the center. If the observation are close to the center (usually the arithmetic mean or median), we say that dispersion, scatter or variation is small. If the observations are spread away from the center, we say dispersion is large.

Suppose we have three groups of students who have obtained the following marks in a test. The arithmetic means of the three groups are also given below:

Group A: 46, 48, 50, 52, 54        

Group B: 30, 40, 50, 60, 70        

Group C: 40, 50, 60, 70, 80      

In a group A and B arithmetic means are equal i.e. . But in group A the observations are concentrated on the center. All students of group A have almost the same level of performance. We say that there is consistence in the observations in group A. In group B the mean is 50 but the observations are not closed to the center. One observation is as small as 30 and one observation is as large as 70. Thus there is greater dispersion in group B. In group C the mean is 60 but the spread of the observations with respect to the center 60 is the same as the spread of the observations in group B with respect to their own center which

is 50. Thus in group B and C the means are different but their dispersion is the same. In group A and C the means are different and their dispersions are also different. Dispersion is an important feature of the observations and it is measured with the help of the measures of dispersion, scatter or variation. The word variability is also used for this idea of dispersion.

The study of dispersion is very important in statistical data. If in a certain factory there is consistence in the wages of workers, the workers will be satisfied. But if some workers have high wages and some have low wages, there will be unrest among the low paid workers and they might go on strikes and arrange demonstrations. If in a certain country some people are very poor and some are very high rich, we say there is economic disparity. It means that dispersion is large. The idea of dispersion is important in the study of wages of workers, prices of commodities, standard of living of different people, distribution of wealth, distribution of land among framers and various other fields of life.

Some brief definitions of dispersion are:

The degree to which numerical data tend to spread about an average value is called the dispersion or variation of the data.

Dispersion or variation may be defined as a statistics signifying the extent of the scatteredness of items around a measure of central tendency.

Dispersion or variation is the measurement of the scatter of the size of the items of a series about the average.

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