Friday, February 22, 2013

Dibrugarh University - Business Statistics 2010 (Solved)


Answer of Q.N.1(a).

Primary Data: Data which are collected for the first time for a specific purpose are known as Primary data. For example: Population census, National income collected by government, Textile Bulletin (Monthly), Reserve bank of India Bulletin (Monthly) etc.

Methods of collecting primary data:-
(a)  Direct Personal Observation
(b) Indirect Oral Investigation
(c) Schedule and questionnaire
(d) Local reports

Indirect Oral Investigation: Under this method, the investigator collects the data from third parties capable of supplying the necessary information. Sometimes the information’s refuse to give answer to some direct questions, the information’s are then collected by putting some indirect questions on informants OR by interviewing several third persons or witnesses who are expected to know the full knowledge about the problems under study. E.g. when the businessman are reluctant to give information’s about their income to income tax authorities then the authorities (i.e. officers) can get the required information’s from the persons like salesman, clerks etc who directly involve in that business.

Advantages:This methods saves time and money because only those persons are interviewed who know the full facts. Proper training and tactfulness of the investigator may produce good results.

Disadvantages:The investigator takes too much time in convincing the persons to supply information’s. In many cases people do not co-operate and refuse to supply the needed information’s.

Answer of Question no. 1(d).
Primary Data: Data which are collected for the first time for a specific purpose are known as Primary data. For example: Population census, National income collected by government, Textile Bulletin (Monthly), Reserve bank of India Bulletin (Monthly) etc.

Secondary Data: Data which are collected by someone else, used in investigation are knows as Secondary data. Data are primary to the collector, but secondary to the user. For example: Statistical abstract of the Indian Union, Monthly abstract of statistics, Monthly statistical digest, International Labour Bulletin (Monthly).

Methods of collecting primary data:
(a)  Direct Personal Observation
(b) Indirect Oral Investigation
(c) Schedule and questionnaire
(d) Local reports
Direct personal investigation:In this method the investigation interview. The concerned persons on the spot about the problems under study and record the required information’s personally.

Advantage: The data obtained by this method are highly accurate and reliable and reliable. The accuracy of the results depends on the efficiency and proper training of the investigator. The investigator should be polite, tactful and conversant. He should mix himself with the people and speak the language of the people. In this way he can get maximum information’s about the problem under study.

Disadvantages: This methods is very slow, expensive and time consuming and particularly suitable for small scale and secret inquiries. The personal like and dislike of the investigator may surely affect the result.

Indirect Oral Investigation: Under this method, the investigator collects the data from third parties capable of supplying the necessary information. Sometimes the information’s refuse to give answer to some direct questions, the information’s are then collected by putting some indirect questions on informants OR by interviewing several third persons or witnesses who are expected to know the full knowledge about the problems under study. E.g. when the businessman are reluctant to give information’s about their income to income tax authorities then the authorities (i.e. officers) can get the required information’s from the persons like salesman, clerks etc who directly involve in that business.

Advantages:This methods saves time and money because only those persons are interviewed who know the full facts. Proper training and tactfulness of the investigator may produce good results.

Disadvantages:The investigator takes too much time in convincing the persons to supply information’s. In many cases people do not co-operate and refuse to supply the needed information’s.

Answer of Question no. 2(c)

Properties of the Correlation Coefficient
a)      The correlation coefficient is symmetrical with respect to X and Y i.e. rXY=rYX
b)      The Correlation coefficient is a pure number and it does not depend upon the units in which the variables are measure.
c)       The correlation coefficient is the geometric mean of the two regression coefficients. Thus if the two regression lines of Y on X and X on Y are written as Y=a+bx and X=c+dy respectively then bd=r2.
d)      The correlation coefficient is independent of the choice of origin and scale of measurement of the variables, i.e. r remains unchanged if constants are added to or subtracted from the variables and if the variables having same size are multiplied or divided by the class interval size.
e)      The correlation coefficient lies between -1 and +1, symbolically -1≤r≤1.

Importance of Statistics
a)      It presents fact in a definite form. Numerical expressions are convincing and, therefore, one of the most important functions of statistics is to present statement in a precise and definite form.

b)      It simplifies mass of figures. The data presented in the form of table, graph or diagram, average or coefficients are simple to understand.

c)       It facilitates comparison. Once the data are simplified they can be compared with other similar data. Without such comparison the figures would have been useless.

d)      It helps in prediction. Plans and policies of organisations are invariably formulated in advance at the time of their implementation. knowledge of future trends is very useful in framing suitable policies and plans.

e)      It helps in formulating and testing hypothesis. Statistical methods like z-test, t-test, X2-test are extremely helpful in formulating and testing hypothesis and to develop new theories.

f)       It helps in the formulation of suitable policies. Statistics provide the basic material for framing suitable policies. It helps in estimating export, import or production programmes in the light of changes that may occur.

g)      Statistics indicates trend behavior. Statistical techniques such as Correlation, Regression, Time series analysis etc. are useful in forecasting future events.

Answer of Question no. 4(a).
Utility of Time Series Analysis
The analysis of Time Series is of great significance not only to the economist and businessman but also to the scientist, geologist, biologist, research worker, etc., for the reasons given below:

a)      It helps in understanding past behaviors: By observing data over a period of time one can easily understanding what changes have taken place in the past, Such analysis will be extremely helpful in producing future behavior.

b)      It helps in planning future operations: Plans for the future cannot be made without forecasting events and relationship they will have. Statistical techniques have been evolved which enable time series to be analyzed in such a way that the influences which have determined the form of that series to be analyzed in such a way that the influences which have determined the form of that series may be ascertained.

c)       It helps in evaluating current accomplishments: The performance can be compared with the expected performance and the cause of variation analyzed. For example, if expected sale for 1995 was 10,000 refrigerators and the actual sale was only 9,000, one can investigate the cause for the shortfall in achievement. Time series analysis will enable us to apply the scientific procedure for such analysis.

d)    It facilitates comparison: Different time series are often compared and important conclusions drawn there from. However, one should not be led to believe that by time series analysis one can foretell with 100percnet accuracy the course of future events.

Answer of Question no. 4(d).
(i) Method of Least Square
This method is most commonly used method of measuring trend. It is a mathematical method and a trend line is fitted to the data in such a manner that the following two conditions are satisfied:-
i) the sum of deviation of the actual values from their respective mean is zero.
ii) the sum of square of the deviations of the actual and compute values is least from this line. That is why this method is called method of least square. The straight line trend is represented by the equation:
Y = a + bx
Where, y = denotes the trend values
                a = represents the intercept on y axis.
                b= represents slope of the trend line.
Merits:
i) This is a mathematical method of measuring trend.
ii) Trend values can be obtained for all the given time periods in the series.
Demerits:
i) This method is more tedious and time consuming.
ii) This method cannot be used to fit the growth curves.

(ii) Simple-average method
Under this method, the given data is divided into two parts. After that an average of each part is obtained which gives two points. Each point is plotted at the mid-point of the class interval covered by the respective part and then the two points are joined by a straight line which gives the required trend line.

Merits:
i) This method is simple to understand as compared to the moving average method and the method of least square.
ii) This is an objective method of measuring trend as everyone who applies this method gets the same result.
Demerits:
i) It is affected by extreme values.
                ii) This method assumes straight relationship between the plotted points whether this exist or not.

(iii) Method of moving average
Under this method the average value for a certain time span is secured and this average is taken as the trend value for the unit of time falling at the middle of the period covered in the calculation of the average. While using this method it is necessary to select a period for moving average.
Merits:
i) This method is simple to understand and apply.
ii) It is particularly effective if the trend of a series is very irregular.
iii) It is a flexible method of measuring trend because all figures are not changed if a few figures are added to the data.
Demerits:
i) Trend values cannot be computed for all years.
ii) No there is no hard and fast rule for selecting the period of moving average.
iii) this method is not appropriate if the trend situation is not linear.

Answer of Question no. 5(b).

Steps in forecasting
The forecasting of business fluctuations consists of the following steps:

a)      Understanding why changes in the past have occurred: One of the basic principles of statistical forecasting is that the forecaster should use the data on past performance. The current rate and changes in the rate constitute the basis of forecasting. Once they are known, various mathematical techniques can develop projections from them. If an attempt is made to forecast business fluctuations without understanding why past changes have taken place, the forecast will be purely mechanical.

b)      Determining which phases of business activity must be measured: After understanding the reasons of occurrence of business fluctuations, it is necessary to measure certain phases of business activity in order to predict what changes will probably follow the present level of activity.

c)       Selecting and compiling data to be used as measuring devices: There is an independent relationship between the selection of statistical data and determination of why business fluctuations occur. Statistical data cannot be collected and analysed in an intelligent manner unless there is a sufficient understanding of business fluctuations. It is important that reasons for business fluctuations be stated in such a manner that is possible to secure data that are related to the reasons.

d)      Analysing the data: Lastly, the data are analysed in the light of understanding of the reason why change occurs. For example, if it is reasoned that a certain combination of forces will result in a given change, the statistical part of the problem is to measure these forces, from the data available, to draw conclusions on the future course of action. The methods of drawing conclusions may be called forecasting techniques.

Answer of Question no. 5(c)

Time series analysis
Time series analysis is also used for the purpose of making business forecasting. The forecasting through time series analysis is possible only when the business data of various years are available which reflects a definite trend and seasonal variation. By time series analysis the long term trend, secular trend, seasonal and cyclical variations are ascertained, analysed and separated from the data of various years.

Merits and demerits of time series analysis
Merits
Demerits
It is an easy method of forecasting.
This method is expensive, difficult and time taking.
By this method a comparative study of variations can be made.
This method deals with past data only.
Reliable results of forecasting are obtained as this method is based on mathematical model.
This method can only be used when the data for several years are available.

Regression analysis
Regression analysis is the most popular method of forecastin. It is the measure of the average relationship between two or more variable in terms of the original units of the data.It is a statistical tool with the help of which the unknown values of one variable can be estimated from known values of another variable.

Merits and demerits of Regression  analysis
Merits
Demerits
The study of regression helps the statisticians to estimate the most probable value of one variable of a series for the given values of the other related variables of the series.
Regression analysis is based on the assumption that while computing regression equation; the relationship between variables will not change.
Regression is useful in describing the nature of the relationship between two variables .
The application of regression analysis is based on certain conditions like, for existence of linear relationship between the variables; exact values are needed for the independent variable.
Regression analysis is widely used for the measurement and estimation of relationship among economic variables.
There may be nonsense and spurious regression relationships. In such case, the regression analysis is of no use.


Answer of Question no. 5(d).
Theories of Business Forecasting
There are a few theories that are followed while making business forecasts. Some of them are:
a.       Sequence or time-lag theory
b.      Action and reaction theory
c.       Economic rhythm theory
d.      Specific historical analogy
e.      Cross-cut analysis theory

Sequence or time-lag theory: 
This is the most important theory of business forecasting. It is based on the assumption that most of the business data have the lag and lead relationships, that is, changes in business are successive and not simultaneous. There is time-lag between different movements. The table 13.5 lists the merits and demerits of sequence or time-lag theory.

Merits and demerits of sequence or time-lag theory
Merits
Demerits
This method is largely used for business forecasting because of the accuracy.
This method studies only the action not the reaction.
Though this theory is based on statistical techniques, yet it is easy to understand.
This method cannot be regarded as accurate because by using statistical techniques the results can be up to the truth but not an accurate one.
Time-interval between two events can be ascertained.

Government can use this technique for the purpose of economic stability of the economy by exercising control over possible losses.


Action and reaction theory: This theory is based on the following two assumptions.
a)      Every action has a reaction
b)      Magnitude of the original action influences the reaction

Thus, if the price of rice has gone up above a certain level in a certain period, there is a likelihood that after some time it will go down below the normal level. Thus, according to this theory a certain level of business activity is normal or abnormal; conditions cannot remain so for ever. Thus, we find four phases of a business cycle. They are:
i. Prosperity
ii. Decline
iii. Depression
iv. Improvement

Merits and demerits of action and reaction theory
Merits
Demerits
This is better than other theories.
The determination of normal level is very difficult.
By this theory more reliable results can be obtained because this theory gives attention to action and reaction of an event.
It is not necessary that reaction is equal to the action.

Economic rhythm theory:
The basic assumption of this theory is that history repeats itself and hence assumes that all economic and business events behave in a rhythmic order.
According to this theory, the speed and time of all business cycles are more or less the same and by using statistical and mathematical methods, a trend is obtained which will represent a long term tendency of growth or decline. It is done on the basis of the assumption that the trend line denotes the normal growth or decline of business events.

Merits and demerits of economic rhythm theory
Merits
Demerits
Forecasting is made on the basis of past conditions, hence they are more reliable.
The business events are not strictly periodic and prediction of business cycle on the basis of statistical method is not satisfactory.
This method is helpful in long-term forecasting.
Past conditions are given more weightage than the present conditions.

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