# Dibrugarh University - Business Statistics 2011 (Solved)

Answer of Question no. 1 (a).
Difference between Primary Data and Secondary Data:
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).
Some of the differences of Primary Data and Secondary Data are given below:
a)      Primary data are those which are collected for the first time and thus original in character. While Secondary data are those which are already collected by someone else.
b)      Primary data are in the form of raw-material, whereas Secondary data are in the form of finished products.
c)       Primary data are collected directly from the people related to enquiry while Secondary data are collected from published materials.
d)      Data are primary in the hands of institutions collecting it while they are secondary for all others.

Answer of Question no. 1 (c).
Measure of dispersion may be broadly classified into two types:
a)      Absolute measures of dispersion: It is classified into
(i)      Range
(ii)    Mean Deviation
(iii)   Standard Deviation
(iv)  Quartile Deviation

b)      Relative measures of dispersion: It is classified into
(i)      Coefficient of Range
(ii)    Coefficient of Mean Deviation
(iii)   Coefficient of Variation
(iv)  Coefficient of Quartile Deviation.

Difference between absolute and relative measure of dispersion:
a)      Absolute measures are dependent on the unit of the variable under consideration whereas the relative measures of dispersion are unit free.

b)      For comparing two or more distributions, relative measures and not absolute measures of dispersion are considered.

c)       As compared to absolute measures of dispersion, relative measures of dispersion are difficult to compute and comprehend.

Regression line
A line of regression by the method of “least square” shows an average relationship between variables under study. This regression line can be drawn graphically or derived algebraically. A line fitted by method of least square is known as the line of best fit. There are two regression lines:-
Regression line of x on y: - Regression line of x on y is used to predict x for a given value of y. The regression equation of x on y is x=a+by.
Regression line of y on x: - Regression line of y on x is used to predict y for a given value of x. The regression equation of y on x is y=a+bx
Two regression lines:
There are two lines of regression: - x on y and y on x. For these lines, the sum of the square of the deviations between the given values and their corresponding estimated values obtained from the line is least as compared to other line. One regression line cannot minimise the sum of squares for both the variables that is why we are getting two regression lines. (We get one regression line when r = +1 and Two regression lines will be at right angles when r = 0.)

Correlation and Regression
Correlation is the degree of the relationship between two or more variables. It does not explain the cause behind the relationship.
Regression 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.
There are some basis difference between correlation and regression:
(1) Nature of relationship: - Correlation explains the degree of relationship, whereas regression explains the nature of the relationship.
(2) Causal relationship: - Correlation does not explain the cause behind the relationship whereas regression studies the cause and effect relationship.
(3) Prediction: - Correlation does not help in making prediction whereas regression enable us to make prediction.
(4) Origin and scale: - Correlation coefficient is independent of the change of origin and scale, whereas regression coefficient is independent of change of origin but not of scale.

Index Number
Index number is an indicator of changes in prices and quantities. It is a specialized average designed to measure the change in a group of related variables over a period of time. It is also an indicator of inflationary or deflationary tendencies.

Uses of Index number:
a)      Measurement of change in the price level or the value of money: - Index number can be used to know the impact of the change in the value of money on different sections of the society.

b)      Knowledge of the change in standard of living: - Index number helps to ascertain the living standards of people. Money income may increase but if index number show a decrease in the value if money. Living standard may even decline.

c)       Adjustment in salaries and allowances: - Cost of living index number is a useful guide to the government and private enterprises to make necessary adjustment in salaries and allowances of the workers.

d)      Useful to business community: - Price index numbers serve as a useful guide to the business community in planning.

e)      Information regarding foreign trade: - Index of exports and imports provides useful information regarding foreign trade.

Limitation of index number
a)      Not completely true: - Index number not fully true. The index number simply indicate arithmetical tendency of the temporal changes in the variable.

b)      International comparison is not possible: - Different countries have different bass of index numbers; these do not help international comparisons.

c)       Difference of time: - With the passage of time, it is difficult to make comparison of index number. With the changing time man’s habits.

d)      Limited use: - Index numbers are prepared with certain specific objective. If they are used for another purpose they may lead to wrong conclusion.

e)      Lack of retail price index number: - Most of the index numbers are prepared on the basis of wholesaler prices. But in real life, retail prices are most relevant, but it is difficult to collect retail prices.

Components of time series
1. Secular trend: - Secular trend is a long term trend which has the basic tendency to grow or decline over a period of time. It may be due to population change technological progress, large scale shifts in consumer tastes, discovery of new things, etc.

2. Seasonal variation: - Seasonal variations are those periodic movements in business activity, which occur regularly every year and have their origin in the nature of the year itself. It may be due to climate weather conditions, customs, traditions and habits, festivals, etc.

3. Cyclical variation: - The term cycle refers to the recurrent variations in time series that usually last longer than a year and are regular neither in amplitude nor in length. Cyclical fluctuations are long-term movements that represent consistently recurring rises and declines in activity. It has four important characteristics:
i) Prosperity
ii) Decline
iii) Depression
iv) Improvement

4. Irregular variation or irratic movement: - It is the variation in business activities, which do not repeat in a definite pattern. Floods, earthquakes, strikes and wars cause it.

Methods for Measuring trends
The following four methods are commonly used for measuring trends:-
i)        Graphic method
ii)       Semi-average method
iii)     Moving average method
iv)     Method of least squares.

i) Graphic method: - This is the simplest method of studying trend. The procedure of obtaining a straight line trend is:
a) Plot the time series on a Graph.
b) Examine the direction of the trend based on the plotted information.
c) Draw a straight line which shows the direction of the trend.
The trend line thus obtained can be extended to predict future values.

ii) Semi-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.

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.

iv) 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.

Business forecasting refers to the analysis of past and present economic conditions with the object of drawing inferences about probable future business conditions. The process of making definite estimates of future course of events is referred to as forecasting and the figure or statements obtained from the process is known as ‘forecast’ future course of events is rarely known. In order to be assured of coming course of events, help is taken of an organised system of forecasting.
(a) Future Prediction: Forecasting is a part of human conduct. Businessmen also need to look to the future. Success in business depends on correct predictions. In fact when a man enters business, he automatically takes with it the responsibility for attempting to forecast the future.
To a very large extent, his success or failure would depend upon the ability to successfully forecast the future course of events. Without some element of continuity between past, present and future, there would be little possibility of successful prediction. But history is not likely to repeat itself and we would hardly expect economic conditions next year or over the next ten years to follow a clear cut prediction. Yet, frequently past patterns prevail sufficiently to justify using the past as a basis for predicting the future.
(b) Reducing Uncertainty:  A businessman cannot afford to base his decisions on guesses. Forecasting helps a businessman in reducing the areas of uncertainty that surround management decision making with respect to costs, sales, production, profits, capital investment, pricing, expansion of production, extension of credit, development of markets, increase of inventories and curtailment of loans. These decisions cannot be made off-hand. They are to be based on present indications of future conditions.
(c) Measurement of Risk: However, we should know that it is impossible to forecast the future precisely. There is a possibility of occurrence of some range of error in the forecast. Statistical forecasts are the methods in which we can use the mathematical theory of probability to measure the risks of errors in predictions.
There are two assumptions:
i) There is no sudden jump in figures from one period to another
ii) There is regularity in fluctuations and the rise and fall is uniform

Methods of Business Forecasting: The following are the main methods of business forecasting.
2.       Time series analysis
3.       Extrapolation
4.       Regression analysis
5.       Modern econometric methods
6.       Exponential smoothing method

Business barometers:  Business indices are constructed to study and analyse the business activities on the basis of which future conditions are predetermined. As business indices are the indicators of future conditions, so they are also known as “business barometers” or ‘economic barometers’. With the help of these business barometers the trend of fluctuations in business conditions are made known and by forecasting a decision can be taken relating to the problem.
The construction of business barometer consists of gross national product, wholesale prices, consumer prices, industrial production, stock prices, and bank deposits. These quantities may be converted into relatives on a certain base. The relatives so obtained may be weighted and their average is computed. The index thus arrived at in the business barometer.

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.

Extrapolation: Extrapolation is the simplest method of business forecasting. By extrapolation, a businessman finds out the possible trend of demand of his goods and also about the future price trends. The accuracy of extrapolation depends on two factors:
i) Knowledge about the fluctuations of the figures
ii) Knowledge about the course of events relating to the problem under consideration
Thus, there are two assumptions on which extrapolations are based:
i) There is no sudden jump in figures from one period to another
ii) There is regularity in fluctuations and the rise and fall is uniform
In extrapolation, we assume that the variable will follow the established pattern of growth. For the purpose of business forecasting, it is to determine accurately the appropriate trend curve and the values of its parameters.

Business forecasting refers to the analysis of past and present economic conditions with the object of drawing inferences about probable future business conditions. The process of making definite estimates of future course of events is referred to as forecasting and the figure or statements obtained from the process is known as ‘forecast’ future course of events is rarely known. In order to be assured of coming course of events, help is taken of an organised system of forecasting. The following are two aspects of scientific business forecasting.
a)      Analysis of past economic conditions
b)      Analysis of present economic conditions

(a) Future Prediction
(b) Reducing Uncertainty
(c) Measurement of Risk

a)      Based on past and present conditions: Business forecasting is based on past and present economic condition of the business. To forecast the future, various data, information and facts concerning to economic condition of business for past and present are analysed.

b)      Based on mathematical and statistical methods: The process of forecasting includes the use of statistical and mathematical methods. By using these methods, the actual trend which may take place in future can be forecasted.

c)       Period: The forecasting can be made for long term, short term, medium term or any specific period.

d)      Estimation of future: The business forecasting is to forecast the future regarding probable economic conditions.

e)      Scope: The forecasting can be physical as well as financial.

Sales Forecasting
In general terms, forecasting means “A statement made about the future”. So, Sales forecasting is the estimation of sales made for the future. Sales forecast is an estimate of sales in rupees or in units for future period. A sales forecast is the prediction of sales volume that a company can estimate to achieve in specified period of time in future.
According to American marketing Association, “Sales forecast is an estimate of sales in dollars (Rupees in India) or physical units for a specified future period”.
Sales forecasting is the basis of all business activities. All the business activities may it a sales related matter, production related matter, finance, advertising, etc depend on sales forecasting. Any business firm starts its plan with sales forecasting .Sales forecasting is a self-assessment tool for a company. The future direction of the company depends on sales forecasting.  The importance of Sales forecasting can be stated as follows:
a)      Overstocking and under stocking of materials can be maintained by a good inventory control.
b)      With the help of sales forecasting, sales opportunities can be found out on the basis of the forecast.
c)       All the activities in an organization are controlled on the basis of forecasting.
d)      Advertising and sales promotion expenses are based on sales forecasting.
e)      Sales forecasting is also important in the field of personnel department. The number of sales persons, executives etc can be increased or decreased on the basis of sales forecasting.

Demand Forecasting
Forecasting is the process to predict how the future needs, which include the requirement in the size of the quantity, quality, time and location that is required in order to meet the demand for goods or services.
Demand Forecasting is the demand for products that are expected to be realized for a certain period in the future. Inforecasting we must pay attention to forecasting procedures should be implemented, namely :
Determining the purpose of forecasting.
a)      Choose the item “independent demand” to be predicted. Plot data intoscatter diagram.
b)      Selecting “forecasting method” in accordance with the pattern of data for its intended purpose.
c)       Counting errors are to be performance of each method used, can be known.
d)      The selection of the best method, which has the smallest error rate.
e)      Make predictions of future demand, then perform the test verifies that the forecasting results carried out a representative to the past data