BBA104 BB0035–Quantitative Techniques in Business

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Bachelor of Business Administration-BBA Semester II

BBA104/BB 0035–Quantitative Techniques in Business

Assignment Set- 1

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

drafting a questionnaire?

b. What do you mean by classification? What purpose does it serve?

ANSWER: The ‘questionnaire’ is a proforma containing a sequence of questions relevant to a statistical enquiry. Since the questionnaire is the only medium of communication between the investigator and the respondents, it must be designed or drafted with utmost care and caution so that all relevant and essential information for the enquiry may be collected without any difficulty, ambiguity, and vagueness. Designing a questionnaire, therefore, requires a high degree of skill and experience on the part of the investigator. The following points should be observed in drafting the questionnaire:

1) The questionnaire should be as short as possible. Many questions may arise during an investigation. But if all are included, the questionnaire will become unduly lengthy with the consequence that the respondents (i.e., persons who are required to answer them) will feel bored and reluctant to answer all the questions.

2) The individual questions should be simple, unambiguous and precise. Lengthy questions cause irritation, resulting in careless and inaccurate replies. Complicated questions should be split up into several smaller parts which can be easily answered by the respondents. Explanations and definition of some of the terms used in questionnaire must therefore accompany each proforma.

3) If possible, questions should be so set as to elicit only two possible definite answers-‘yes’ or ‘no’.

4) The units in which the information is to be collected should be clearly and precisely mentioned in the questionnaire.

5) The arrangement of questions in the proforma should be such as to have an easy and systematic flow of answers in turn. Questions should not skip back and forth from one topic to another.

6) After the questionnaire has been devised, it is desirable to try it on a few individuals. The procedure, which is known as pilot survey, is useful in detecting the shortcomings of the questionnaire, so that necessary modifications may be made before it is used in the actual enquiry.

Hence, the outcome of each question will produce the large data base. Statistician will use this data base for further analysis and prediction of the results.

Classification is the process of arranging the collected statistical information under different categories or classes according to some common characteristics possessed by the individual members. Statistical data collected during the course of an investigation are so varied that it is not possible to appreciate, even after a careful study, the true significance of the figures, unless they are arranged properly. To make the data really useful, they must be classified or grouped into homogenous categories, so that the like will go with the like and the unlike with the unlike. Classification prepares the ground for enabling comparison and analysis by instituting a logical and orderly arrangement of data. For example, during the population census, apart from the number of members in each family, various other information, e.g., age, sex, occupation etc., of all people in the country are collected. The total population is then classified according to sex into males and females; according to age groups 0-10 years, 10-20 years, etc.; according to livelihood into agricultural classes, production other than cultivation, business, transport, etc. If such classifications are not made, it will not be possible to analyze the data and reveal their true significance from the heaps of material collected during the population census.

There are four types of classification of data:

1) On qualitative basis – Classification of the total population of a country on the basis of sex, religion, occupation etc., belong to this type. This is also known as classification by attributes.

2) On quantitative basis – Classification of the total population according to age, or of industries according to the number of persons employed, etc., is included in this type. Here, the basis of classification is some variable, and hence this is also known as classification by variables.

3) On time basis – Some statistical data are arranged in order of their time of occurrence. Production of a factory may be shown by weeks, months, quarters or years. Statistical data classified according to time are known as time series.

4) On geographical basis – The total population of a country may be classified by states or districts, exports of a particular commodity from India may be classified by the country to which exported. The basis of classification in such cases is by geographical regions.

Q.2. what do you mean by measures of dispersion? What purpose do they serve?

b. What are the characteristics of a good measure of dispersion?

ANSWER: The word dispersion is used to describe the “degree of heterogeneity” in the data. It is an essential characteristic indicating the extent to which observations vary among themselves. The dispersion of a given set of observations will be zero only when all of them are equal.

A business head may be interested to know the average sales of each product and the amount of fluctuations in average sales because he is not only interested in the average level of performance but also in the variability of such performance. By knowing the variability he can take into consideration this aspect for decision making purposes.

Various measures of dispersion can be classified into two broad categories:

· The measures which express the spread of observations in terms of distance between the values of selected observations. These are also termed as distance measures, e.g. range, inter-quartile range etc.

· The measures which express the spread of observations in terms of the average deviations of observations from some central value. These are known as mean deviation, standard deviation etc.

· Both categories of measures can be further classified into absolute and relative measurement of dispersion. Absolute measures of dispersion are: Range, Quartile deviation, Mean Deviation, and Standard deviation. Relative measures are Coefficient of variation, Co-efficient of Quartile deviation, and Co-efficient of Mean deviation. An absolute measure of dispersion is expressed in terms of the unit measurement of variable. A disadvantage of this measure is that it cannot be used to compare dispersions of two or more distributions expressed in different units. Relative measures are obtained by expressing an absolute measure as percentage of a measure of central tendency and hence relative measures are independent of the units of measurement. Usually the absolute measures are employed for measuring dispersion. But for purposes of comparing the dispersion in different series, relative measures are used. Again when two sets of data are given in dissimilar units, there is no other alternative but to use a relative measure for comparison. Relative measures may also be used to compare the relative accuracy of data. But absolute measures cannot be used to compare the relative accuracy of data.

A measure of dispersion is used to test the reliability of an average. A low value of dispersion indicates that there is greater degree of homogeneity among various items and, consequently, their average can be taken as more reliable or representative of the distribution.

To compare the extent of the variability in two or more distributions

The extent of variability in two or more distributions can be compared by computing their respective dispersions.

To facilitate the computation of other statistical measures

Measures of dispersions are used in computations of various important statistical measures like correlation, control limits etc.

A good measure of dispersion should possess the following characteristics:

i) It should be easy to calculate.

ii) It should be easy to understand.

iii) It should be based on all observations.

iv) It should be rigidly defined.

v) It should be capable of further analysis.

vi) It should not be much affected by the fluctuations of sampling.

Q.3. What is scatter diagram? How does it help in ascertaining the nature and degree of linear correlation between two variables?

ANSWER:The Scatter diagram

When statistical data relating to the simultaneous measurements of two variables are available, each pair of observations can be geometrically represented by a point on the graph paper. The values of the one variable will be shown along the x-axis and the other variable along Y-axis. If these are n pairs of observations, finally the graph paper will contain n points. This diagrammatic representation of bivariate data is known as scatter diagram.

A scatter diagram of the data helps in having a visual idea about the nature of association between two variables. If the points cluster along a straight line, the association between variables is linear. For example, if the pattern of points on the scatter diagram shows a linear path diagonally across the graph paper from the bottom left hand corner to the top right hand corner, the correlation is positive (Fig.5.2). Otherwise, it is negative (Fig.5.3). Further, if the points cluster along a curve, the corresponding association is non-linear or curvilinear (Fig.5.4). Finally, if the points neither cluster along a straight line nor along a curve (Fig.5.5), there is absence of any association between the variables.

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