24 Short Questions with Answers on “Business Statistics & Data Processing” for Commerce Students:
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1. What are the uses of correlation?
1. Decision maker will come to know the nature of relationship between variables and the degree of the relation.
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2. Getting a quantitative figure for correlation makes the decision-making process, objective.
3. It helps in forecasting and planning because changes in variables and its impact can be estimated beforehand.
4. It helps the researcher in identifying such factors, which can stabilize the economy.
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2. What precautions should be taken care of in applying correlation?
1. It is difficult to distinguish between dependent variables and independent variables.
2. Both the correlated variables are affected by a third variable, which has not been taken into consideration by the researcher.
3. The correlation may be due to chance.
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4. Very high degree of correlation between two variables does not necessarily indicate cause and effect relationship between them.
3. Classify correlation.
Correlation may be classified into the following types:
1. Single and Multiple Correlations:
Only two variables are considered in single correlation, i.e., one independent and another dependent variable. In case of multiple correlations, the relation between more than two variables is judged.
2. Partial and Total Correlation:
In the case of partial correlation, relations of two or more variables are considered assuming other variables to be constant. Total correlation is based on all the variables without assuming any variables to be constant.
3. Linear and Non-linear Correlation:
When variation in the values of two variables has a constant ratio, there will be linear correlation between them. In non-linear correlation, the amount of change in one variable does not bear a constant ratio to the amount of change in the other related variable.
4. What methods are used to determine correlation?
Following methods are used to determine correlation:
(a) Scatter diagram.
(b) Karl Pearson’s coefficient of correlation.
(c) Spearman’s Rank coefficient of correlation
5. What are the merits of scatter diagram?
Scatter diagram is easy to understand. Even a layman who is not trained in mathematics or statistics can understand scatter diagram. If the correlation is fairly apparent, then it can be shown through scatter diagram rather than by calculating through mathematical formula.
6. What are the demerits of scatter diagram?
This method does not give any quantitative figure of the degree of correlation. Hence comparison of different data and their correlation are not possible. Scatter diagram is not an objective method of measuring correlation.
7. Write the merits of coefficient of correlation.
1. In one figure of r both the degree of correlation and its direction can be calculated
2. It can be derived from the use of standard deviation.
3. It is closely related to regression analysis.
4. Probable error and standard error can be calculated from coefficient of correlation.
8. What are the limitations of coefficient of correlation?
1. It assumes a linear relationship between independent and dependent variables, which may not always be true.
2. It is applicable only if the distribution is normal
3. The value of the coefficient is unduly affected by extreme items.
4. It is difficult to calculate.
5. It is difficult to understand.
9. Why and how is correction for tied ranks applied in Spearman’s rank correlation method?
In Spearman’s rank-correlation method, the biggest item gets the first rank, the next to it gets second rank and soon. But difficulty may be encountered where two or more items are of equal value. In such cases, correction has to be applied. ^ has to be added to Sd2. ‘m’ is the number of times a particular value of x and y has been repeated. Separate correction has to be applied for each separate case of repetition of ranks.
10. What is binariate frequency table?
If in a binariate distribution the data are fairly large, they may be summarized in the form of a two-way table. For each variable the values are grouped into various classes, keeping in view the same considerations. For example, if there are n classes for the x-variable series and m classes for the y- variable series then there will be m * n cells in two-way table. By going through the different pairs of the values (x, y) and using tally marks we can find the frequency for each and thus obtain the so called binariate frequency table.
11. What is rank correlation method?
Sometimes we come across statistical series in which the variables under consideration are not capable of quantitative measurement but can be arranged in serial order. This happens when we are dealing with qualitative characteristics such as honesty, beauty, character, morality, etc. which cannot be measured quantitatively but can be arranged serially. Spearman’s rank correlation coefficient is denoted by p (Rho) and is given by the formula.
12. What is the method of concurrent deviations for measuring correlation?
This method is based on the signs of the deviations (i.e. direction of the change) of the values of the variable from its preceding value and does not take into account the exact magnitude of the values of the variables. Thus we put a plus (+) sign, minus (-) sign or equality (=) sign for the deviation if the value of the variable is greater than, less than or equal to the preceding value The deviations in the values of two variables are said to be concurrent if they have the same sign i.e. either both deviations are positive or both are negative or both are equal.
13. What is regression?
In the general sense, regression means the estimation or prediction of the known value of one variable from the known value of the other variable. It is especially used in business and economics to study the relationship between two or more variables that are related causally and for estimation of demand and supply curves, cost functions, production and consumption functions, etc. Regression analysis is a mathematical measure of relationship between two or more variables in terms of the original units of the data
14. How many types of variables are there in regression analysis?
In regression analysis there are two types of variables. The variable whose value is influenced or is to be predicted is called dependent variable and the variable, which influences the values or is used for prediction is called independent variable.
15. What do you understand by the lines of regression?
Lines of regression of yon x is the line which gives the best estimate for the value of y for any specified value of x. Similarly line of regression of x on y is the line which gives the best estimate for the value of x for any specified value of y. In y on x, y is a dependent variable and x is an independent variable.
In x on y, x is dependent variable and y is an independent variable. The two regression equations are not reversible or interchangeable because the basis and assumptions for deriving these equations are different. The regression equation of y on x is obtained on minimizing the sum of the square of the errors parallel to y-axis while the regression, equation of y on y is obtained on minimizing the sum of squares of the errors parallel to x-axis.
16. What are the uses of F-test?
F-test can be used for the following:
(a) for testing the significance of an observed sample multiple correlation
(b) for testing the significance of an observed sample correlation ratio.
(c) for testing the linearity of regression.
(d) for testing the equality of several population means, i.e. for testing H0= p, = µ2…, µ2 (say) for K normal population
17. Describe various conditions for the validity of chi-square test.
The chi-square test statistic can be used only if the following conditions are satisfied:
1. N, the total frequency, should be reasonably large, say greater than 50.
2. The sample observations should be independent. This implies that no individual item should be included twice or more in the sample.
3. The constraints on the cell frequencies if any, should be linear (i.e. they should not involve square and higher powers of the frequencies.)
4. No theoretical frequency should be small. Preferably each theoretical frequency should be larger than 10 but in any case not less than 5.
5. The given distribution should not be replaced by relative frequencies or proportions but the data should be given in original units.
18. What do you understand by the term ‘data’?
Data refers to a number of facts, figures or statistics about the activities of a business such as hours worked on individual operations, quantity of material issued for specific jobs etc. Data are usually unrelated and sometimes, un-interpreted and hence, not meaningful.
19. What is meant by data processing?
By data processing is meant the processing or handling of the various types of data we come across during the operation and management of a business. Data processing comprises the collection, classification and analysis of data so as to finally create the information to be reported. The processing may be manual, mechanical or electronic. While computers are very often referred to as data processing or electronic data processing system, a simple system of book keeping maintained manually is also a form of data processing system
20. Describe the steps involved in a system of data processing.
The basic steps involved in a system of data processing are as follows:
(i) Collection and recording of data. The data originally recorded in source documents, e.g. clock cards, goods received notes, etc. are transcribed on a suitable data record such as handwritten or typed on a paper form, keypunched on a card, keyed on magnetic tape, etc.
(ii) Arranging and classifying the data recorded. This is done in a desired sequence or order manually, with the help of sorting machines tape, etc.
(iii) Processing the data and summarizing them into suitable heads required in the information or final report. The processing may be manual, mechanical or electronic
21. What is integrated data processing?
Integrated data processing is a unified system in which several phases of data processing in an organization are streamlined into one interlinked system. In other words, the data handled for the various sectors of control of an undertaking e.g. for payrolls, inventory control, production control, cost accounting etc. are integrated into one system so that there is an uninterrupted automatic flow of data in an orderly fashion in all parts of the organization and all levels of management are fed with the information they need.
22. What are the benefits of integrated data processing?
Benefits of integrated data processing are as follows:
(i) Data is properly analysed and shifted, unnecessary items are weeded out, and data are to flow with speed.
(ii) The use of the same co-coordinated data ensures accuracy.
(iii) It gives an overall co-coordinated picture to the management. To cite one example, relationship between sales, purchase, and production is clearly brought out if all the relevant data are properly integrated during processing.
23. What do you mean by electronic data processing?
Electronic data processing (EDP) usually refers to the processing of data through electronic computers, which are electronic devices with associated electro-mechanical equipments. Data collected in a coded form (known as the input) are fed into the computer and processed at very high speeds.
24. What is information?
Information is data that has been processed into a form which is meaningful to the recipient and is of real or perceived value in current or prospective actions or decisions. This definition recognizes both the value of information in a specific decision and the value of information in motivation, model building, and background building affecting future decisions and actions.