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CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
APR2016
ASSESSMENT_CODE MCA4020_APR2016
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID
72290
QUESTION_TEXT
Explain the five important problems involved in the construction of index
number.
SCHEME OF
EVALUATION
1. Purpose if Index Number: The first and important thing is to specify
the purpose of using index number. There are many purpose for which
the index number may be constructed like measure to general price
level changes in a country or to measure the changes in the cost living of
particular section of people or any other.
(2
Marks)
2. Selection of Base year: Base period is defined as the period which
data of any other year is compared to known the percentage of increase
or decrease in changes. The index for the base year is always taken as
100.
While selecting base year following points should be kept in mind:
 The base year should be normal.
 The base year should not be too distant from the given periods.
 Fixed base or chain base
(2 Marks)
3. Selection of Number of items: The next problem in the construction
of index number is the selection of items and their varieties included in
the index should neither be too big nor too
small.
(2 Marks)
4. Selection of data: The data related to set of prices and of quantities
consumed for the selected commodities for different periods, places etc
is used to construct the index numbers. Not that the data should be
collected from reliable sources.
(2 Marks)
5. Selection of appropriate weights: The problem of selecting suitable
weights to different commodities is very important and at the same
time very difficult also as all items is not equally important. There are
two types of indices.
 Unweighted Indices
 Weighted Indices
(2 Marks)
6. Selection of suitable method of averaging: Since index numbers are
specialized average, so need to decide which particular average of
arithmetic mean, median, mode, geometric mean or harmonic mean
should be used for constructing the index number.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72291
a.
What are the requisites of Ideal measure of Dispersion?
b.
List out the Absolute Measure of variation.
QUESTION_TEXT
a)
SCHEME OF
EVALUATION
1.
It should be easy to understand and simple to calculate.
2.
It should be based on all values.
3.
It should be rigidly defined.
4.
It should not be affected by extreme values.
5.
It should not be affected by sampling fluctuations
6. It should be capable of further algebraic
treatment
(6 Marks)
b)
1.
Range:
2.
Quartile Deviation:
3.
Mean Deviation
4.
Standard Deviation
(4 Marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72292
QUESTION_TEXT
Briefly explain the five important laws of sampling theory.
SCHEME OF
EVALUATION
The sampling theory is based on following five important laws.
Law of statistical regularity
Principle of inertia of large numbers
Principle of persistence of small numbers
Principle of validity
Principle of optimization
(2+2+2+2+2)
1. Law of statistical regularity
The Law of statistical regularity states that a group of unit chosen at
random from a large group tends to posses the characteristic of that
large group.
Suppose a particular characteristic of the population has a particular
shape, then the same characteristic will also follow the same shape in
the sample.
2. Principle of inertia of large numbers
This principle states that “other thing being equal, as the sample size
increases, the result tends to be more reliable and accurate”. Suppose
that the population mean is 25 units. If a sample of size 50 results in
average of 24.5 units, then larger sample of size 100 will result in 24.8
units. In other words, larger the sample size, more accurate will be the
result.
3. Principle of persistence of small numbers
If some of the units in a population possess markedly distinct
characteristics, then it will be reflected in the sample values also. For
example if there are 300 blind persons in a population of 1000 persons,
the sample of 100 will have more or less same proportion of blind
persons in it.
4. Principle of validity
A sampling design is said to be a valid if it enables us to obtain tests and
estimation about population parameters.
5. Principle of optimization.
This principle aims at obtaining a desired level of efficiency at minimum
cost or obtaining maximum possible efficiency with given level of cost.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72293
QUESTION_TEXT
Define Correlation and explain its types.
SCHEME OF
EVALUATION
Correlation is the statistical tool used to study the relationship between
two or mare variables. Two variables are said to be correlated if the
change in one variable there will be change in other variable. On the
other hand if the change in one variable does not bring change in other
variable then we say that the two variables are not correlated to each
other.
Types of correlation
There are four types of correlation
1. Simple, partial and multiple correlation.
2. Positive and negative correlation
3. Perfect and imperfect correlation
4. Linear and nonlinear correlation
1. Simple, partial and multiple correlation.
Simple correlation is the relationship between any two variables. Partial
correlation is the study of relationship between any two out of three or
more variables ignoring the effect of other variables. For example let us
suppose that we have three variables X1=marks ma maths, X2= marks
of science, X3= marks of English. So if we study the relationship
between X1 and X2 ignoring the effect of other variable i.e X3, then it is
partial correlation.
Multiple correlation is the study of simultaneous relationship between
one or group of other variables. For example if we study X1, X2, X3
simultaneously then correlation between X1 and (X2, X3) is multiple
correlation. Multiple correlation is not commonly used.
2. Positive and negative correlation.
Two variables are said to be positively correlated when both the
variable under study move in the same direction, i.e if one variable
increases the other variable should also increase and if one variable
decreased other variable should also decrease. Variables are said to be
negatively correlated if increase in one variable leads to decrease in
other variable, and vice versa. That is the variable move in opposite
direction.
For positive correlation the graph will be upward curve where as in case
of negative correlation the graph will be downward curve.
3. Perfect and imperfect correlation.
When both the variables changes at a constant rate irrespective of the
change in direction then it is called perfect correlation. When the
variables changes at different ratio then it is called imperfect
correlation. The values of perfect correlation is 1 or -1. The values of
imperfect correlation lies in between -1 and +1.
4. Linear and nonlinear correlation.
Linear correlation is correlation when the graph of the correlated data is
a straight line. That is the variables are perfectly correlated. The linear
correlation can be either positive or negative when the graph of straight
line is either upward or downward in direction. On the other hand non
linear or curvi-linear correlation is a correlation when the graph of the
variables gives a curve of any direction. Like perfect correlation non
linear correlation can be either be positive or negative in nature
depending upon the upward and downward direction of curve.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72294
QUESTION_TEXT
Briefly explain the different types of probability sampling.
SCHEME OF
EVALUATION
The sampling theory is based on following five important laws.
1. Law of statistical regularity
2. Principle of inertia of large numbers
3. Principle of persistence of small numbers
4. Principle of validity
5. Principle of optimization
(2+2+2+2+2)
1.simple random sampling
under this technique, sample units are drawn in such a way that each
and every unit in the population has an equal and independent chance
of being included in the sample.
If a sample unit is replaced before drawing the next unit, then it is
known as simple random sampling with replace ment[SRSWR]. If the
sample unit is not replaced before drawing the next unit, then it is
called simple random sampling without replacement[SRSWOR]. In first
case, probability of drawing a unit is 1/N, where N is the population
size. In the second case probability of drawing a unit is 1/Nn.
The selection of simple random sampling can be done by
1.lottery method
2.The use of table of random numbers.
2. Stratified random sampling
this sampling desighn is most appropriate if the population is
heterogeneous with respect to charecteristic under study or the
population distribution is highly skewed.
We subdevide the population into several groups or strata such that:
1. units within each stratum is more homogeneous
2. units between strata are heterogeneous.
3. Strata do not overlap, in other words, every unit of population
belongs to one and only one stratum.
The criteria used for stratificationare geographical, sociological, age sex,
income and so on. The population of size 'N' is devided in to 'K' strata
relatively homogeneous of size 'N1', 'N2', . . . 'Nk' such that N1+N2+N3+.
. . +Nk=N'. then, we draw a simple random sample from each stratum
either proportional to size of stratum or equal units from each stratum.
3.Systematic Sampling.
This design is recommended if we have a complete list of sampling units
arranged in some systamatic order such as geographical, chronological
or alphabatical order.
Suppose the population size is 'N'. the population units are serially
numbered '1' to 'N' in some systamatic order and we wish to draw a
sample of n units.
This implies nK=N or K=N/n. From the first group, we select a unit at
random. Suppose the unit selected is 6th unit, thereafter we select
every 6 + Kth units.
4.Cluster Sampling.
The total population is devided into recognisable sub-divisions, known
as clusters such that within each cluster units are more heterogeneous
and between clusters they are homogeneous. The units are selected
from each cluster by suitable sampling techniques.
5. Multi stage sampling.
The total population is devided in to several stages. The sampling
process is carried out through several stages.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
125370
QUESTION_TEXT
Define covariance. State its 8 properties
Covariance is a measure of association between two random
variables. (2mark)
Let X and Y be two random variables. Then the covariance is
defined as
Cov(X,Y)=E[{X-E(X)}{Y-E(Y)}]
=E[XY-XE(Y)-YE(X)+E(X)E(Y)]
=E(XY)-E(Y)E(X)-E(X)E(Y)+E(X)E(Y)
=E(XY)-E(X)E(Y)
Properties : (1+1+1+1+1+1+1+1)
SCHEME OF
EVALUATION
1.
Cov(aX,bY)=abCov(XY)
2.
Cov(X+a,Y+b)=Cov(XY)
3.
Cov(
4.
Cov(aX+b, cY+ d)
5.
Cov(X+Y, Z)=Cov(XZ) + Cov(Y,Z)
6.
7.
V(
,
)=
= acCov(XY)
Cov(aX+bY, cX+dY)= ac
+(ad+bc)
Cov(X,Y)
+ ac
If X1, X2 … Xn be random variable, then
)=
+2
8.
If X1, X2 … Xn be independent random variable random
variable, then
V(
)=