Download BB0010A04

CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
APR2016
ASSESSMENT_CODE BB0010_APR2016
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
8305
QUESTION_TEXT
Explain the Scope and Applications of Statistics?
SCHEME OF
EVALUATION
Statistics is considered to be a distinct branch of study applicable to
investigations in many branches of science. Statistical methods are
applied to specific problems in Biology, Medicine, Agriculture,
Commerce, Business Economics, Industry, Insurance, Sociology,
Psychology etc.
Statistics in Biology, Medicine, Agriculture, etc.; Statistical methods are
in much use in the study of problems associated with Biological
sciences. They are applied in the study of growth of plant, movement of
fish population in the ocean, migration of birds, effect of newly invented
medicines, theories of heredity, estimation of yield of crop, effect of
newly invented medicines, theories of heredity, estimation of yield of
crop, effect of fertilizer on yield, birth rate, death rate, population
growth, growth of bacteria etc. The branch of Statistics which deals with
problems in Biology is Biometry. The branch which deals with problems
relating to population growth is Demography. It is well known that
insurance premiums are based on the age composition of the population
and the mortality rates. Actuarial science deals with the calculation of
insurance premiums and dividends. 5 mark
Statistics is Economics, Commerce, Business etc.; Statistics is part and
parcel of Economics, Commerce and Business. Statistical analysis of
variations of price, demand and production are helpful to businessmen
and economists. Cost of living index numbers help in economic planning
and fixation of wages. They are used to estimate the value of money.
Analysis of demand, price, production costs, inventory cost, etc., help in
decision making in business activities. Management of limited resources
and labour in obtaining maximum profit is done by statistical analysis of
data. Planned recruitments and distribution of staff, proper quality
control methods, careful study of demand for goods in the market,
capture of market by advertisement, balance investment, etc. help the
producer to extract maximum profit out of minimum capital. In
industries, statistical quality control techniques help in increasing and
controlling the quality of products at minimum cost. A government’s
administrative system is fully dependent on production statistics, income
statistics, labour statistics, economic indices of cost, price, etc. Economic
planning of any nature is entirely based on statistical facts. Statistics has
become so important today that hardly any science exists independent of
this, and hence the statement ‘Sciences without Statistics bear no fruit;
Statistics without Sciences has no root’. 5 mark
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
8308
QUESTION_TEXT
What do you mean by Secular Trend?
SCHEME OF
EVALUATION
Secular trend is the long-term tendency of the time series to move in an
upward or downward direction. It summarises the essential life story of
the time series. It indicates how, on the whole, the time series has
behaved over the entire period under study. Also referred to as secular
variations or long-term movements, these are the result of long-term
forces that gradually operate on the time series variable.
A few examples of such forces include long-term changes in
productivity, increase in the rat of capital formation, growth of
population, technological innovations, transformation in socio-economic
setup, etc. Since these forces occur in a slow process, they exert
influence on the time series in a gradual manner.3 mark
The total period which is required to permit the emergence of a trend
depends on (i) the type of event the time series data relate to, and (ii) the
length of the time unit (hour, month, year etc.) against which the data are
recorded. The time period could be as short as a few days or as long as
fifty years, depending on the nature of the even under consideration.
Cyclical Variations
Cyclical variations, also termed as business cycles, are the periodic
movements in the time series around the trend line. These are the
upswings and downswings in the time series that are observable over
extended periods of time. Neither the amplitude nor the frequency of
occurrence of these cycles is uniform. Empirical studies based on the
analysis of time series data on a large number of major economic
aggregates conducted in the United States and other developed countries
have shown that the length of time interval after which cycles occur
ranges from 8 to 10 years.3 mark
Long waves extending up to 50 years have also been observed. These
long waves are difficult to distinguish as they get mixed up with the
trend line. Cycles of 8 to 9 years duration are, however, more common.
These are called trade cycles, while those occurring after a time interval
of 3 to 4 years are known as minor cycles. 2 mark
The forces that give rise to minor cycles cannot be easily listed for being
numerous in number and difficult to separate from those giving rise to
secular variations. Consequently, business cycles are relatively less
predictable than the other types of variations in a time series. 2mark
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
8309
QUESTION_TEXT
Explain the concept of moving average method?
SCHEME OF
EVALUATION
Moving Average Method: This method is more frequently used in
estimating seasonal variations. When applied to estimating trend values,
it does help bring out the trend by eliminating cyclical, seasonal and
random fluctuations in the time series data. It is essentially a non-linear
method as it may not necessary yield a straight line trend. However, if
the pattern of variations in the time series is consistent and uniform both
in terms of amplitude and the interval of occurrence, the moving average
method does yield a near straight line trend.
3 mark
The choice of the length of the period for a moving average is an
important decision as it determines the extent to which the variations
would be smoothed in the process of averaging. Cycles of uniform
length and height can be eliminated more easily by choosing a moving
average period either equal to or multiple of the cycle.3.5 mark
Despite the moving average method being useful under certain
conditions, it suffers from certain drawbacks. It results in loss of values
for some years both in the beginning and at the end of the time series,
depending on the period of moving average. The moving averages also
fail to yield an equation worthy of being used for forecasting the future
values of the time series variable. 3.5 mark
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
73104
QUESTION_TEXT
Define correlation. Write the properties and interpretation of coefficient of correlation.
SCHEME OF
EVALUATION
Two variables are said to be correlated when they vary such that
a) The higher values of one variable correspond to the higher values of the other
and the lower values of the variable correspond to the lower values of the other.
or
b) The higher values of one variable correspond to the lower values of the other. (2
marks)
Properties of coefficient of correlation:
1. The coefficient of correlation is independent of the units of measurement of the
variables.
2. The coefficient of correlation is independent of the origin and scale of
measurement of the variables.
3. The coefficient of correlation is a value between – 1 and +1. (3 marks)
Interpretation of coefficient of correlation:
1. A positive value of r indicates positive correlation.
2. A negative value of r indicates negative correlation.
3. r = +1 means, correlation is perfect positive.
4. r = – 1 means, correlation is perfect negative.
5. r = 0 (or low) means, the variables ae non-correlated. (5 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
117995
QUESTION_TEXT
What is dispersion? Explain briefly the various methods of measuring
variation (Dispersion).
Variation(dispersion) is the property of deviation of values from the average.
The degree variation is indicated by the measures of variation.
Various measures of variation are
SCHEME OF
EVALUATION
i.
ii.
iii.
iv.
Range: Range is the difference between the highest and the lowest
values in the data.
Quartile deviation: The quartile deviation is obtained by dividing the
range between the lower and the upper quartiles by 2.
Mean deviation: The mean deviation of a set of values from a central
value is the mean of absolute deviations of the values from the central
value.
Standard deviation: The standard deviation of a set of values is the
positive square root of mean of the squared deviations of the values
from their arithmetic mean.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
117997
QUESTION_TEXT
What is a population? Mention types of Population. Explain Basic properties of
population.
A Population can be defined as the totality of all possible observations,
measurements or outcomes.
Two types of Population:
SCHEME OF
EVALUATION
i.
Finite Population
ii.
Infinite Population
Basic Properties of Population
i.
Variability in the Elementary Units: Whatever be our target
population, measurements of any characteristics of its elementary units
are subject to variations. These variations are caused by the operation of
multiplicity of complex forces which act and react upon each other and
influence the population units in varying degrees.
ii.
iii.
Variability not without limits: Interestingly, while the variability in the
measurement of the elementary units is a universal property of all
populations, the magnitude of variations is not without limits.
Uniformity in variations: There are multiplicity of complex forces which
generate variations in the elementary units. These forces tend to be so
balanced in their influence that most of the measurements cluster around
a typical central value.