Answer of Question no. 1 (a).
Dispersion and its characterictics
Dispersion: Dispersion is the measure of
variation of items. It measures the extent to which the items vary from central
value. Dispersion is also known as average of the second order.
In the words
of Brooks and Dick,” Dispersion is the degree of the scatter or variation of
the variable about a central value.”
In the words
Simpson and Kafka,” The measurement of the Scatterness of the mass of figures
in a series about an average is called measure of variation or dispersion.”
Dispersion
includes range, mean deviation, quartile deviation, and standard deviation.
The following are the important properties which a good
measure of dispersion should satisfy:
a)
It should be simple to understand and easy to compute.
b)
It should be simple to compute.
c)
It should be based on all the items.
d)
It should not be affected by extreme values.
f)
It should be capable of further algebraic treatment.
g)
It should have sampling stability.
Answer of Question no. 1 (d).
Measure of Central tendency and Its Properties
In the words of Croxton and
Cowden, “An average value is a single value within the range of the data that
is used to represent all the values in the series.”
The value of average lies between
the maximum and minimum values of the series. That is why it is also called
measure of central tendency.
The following are the
important properties which a good average should satisfy
a)
It should be easy to understand.
b)
It should be simple to compute.
c)
It should be based on all the items.
d)
It should not be affected by extreme values.
e)
It should be rigidly defined.
f)
It should be capable of further algebraic treatment.
Sample survey and its advantages
Sample: If a
part is selected out of the universe then the selected part or portion is known
as sample. Sample is only a part of the universe.
Sample survey: It is
a survey under which only a part taken out of the universe is investigated. It
is not essential to investigate every individual item of the Universe.
Advantages of Sample
survey:
a)
It is cheaper as compared to census survey
b)
While using secondary data, time and labour are saved.
c)
It may also be collected from unpublished form.
d)
If secondary Data are available, they are much quicker to obtain than
primary data.
Disadvantages of Sample Survey:
a)
Degree of
accuracy may not be acceptable.
b)
Secondary
Data may or may not fit the need of the project.
c)
Data may be
influenced by personal bias of investigator.
Answer of Question no.2(a).
Properties
of the Correlation Coefficient
a) The
correlation coefficient is symmetrical with respect to X and Y i.e. r_{XY}=r_{YX}
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=r^{2}.
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.
Answer of Question no.2(c).
Plz follow Nag and Chanda book on
statistics. This topic is nicely explained
Answer of Question no. 3(a)
Fisher’s index is regarded as ideal index because:
a)
It considers both base year and
current year’s price and quantity.
b)
It satisfies both time reversal and
factor reversal test.
c)
It is based on Geometric mean which is
theoretically considered to be the best average of constructing index number.
d)
It is free from bias as it considers
both current year and base year price and qty.
Answer of Question no. 3(b)
Difference between Price index and Quantity index
A measure
reflecting the average of the proportionate changes in the prices of a
specified set of goods and services between two periods of time. Usually a
price index is assigned a value of 100 in some selected base period and the
values of the index for other periods are intended to indicate the average
percentage change in prices compared with the base period. A quantity index is
built up from information on prices of various commodities.
A measure
reflecting the average of the proportionate changes in the quantities of a
specified set of goods and services between two periods of time. Usually a
quantity index is assigned a value of 100 in some selected base period and the
values of the index for other periods are intended to indicate the average
percentage change in quantities compared with the base period. A quantity index
is built up from information on quantities such as the number or total weight
of goods or the number of services.
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.
Answer of Question no. 3(c)
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
in Trade and commerce
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.
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(c).
(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) Simpleaverage 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 midpoint
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.
Answer of Question no. 5(a).
Objectives of forecasting
in business:
(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 offhand.
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.
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.

Answer of Question
no. 5(d)
Methods of Business
Forecasting: The following are the main methods
of business forecasting.
1.
Business
barometers
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.