tax reforms committees. · types of kurtosis 1.lepto- kurtic 3.meso-kurtic 2.platy-kurtic it is a...
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Tax reforms committees.
Tax committees and chronological order of taxes.
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1.Measures Of
Kurtosis
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Intro--
Like average, dispersion , skewness and Kurtosis
is forth measure of frequency distribution.
Kurtosis gives idea about the shape of a frequency
distribution.
Kurtosis indicates whether a frequency distribution
is flat, normal and peaked shape.
It refer to degree of flatness or peakedness of a
frequency curve.
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Types of kurtosis
1.Lepto- kurtic
3.Meso-kurtic
2.Platy-kurtic
It is a curve having high peak than normal curve.
Too much concentration the items near the center.
It is a curve having low peak (flat) than the normal curve.
There is less concentration of items near the centre.
It is a curve having normal peak or the normal curve.
There is equal distribution of items around the central
value.
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Lepto-kurtic
Meso-kurtic
platy-kurtic
x̄=M=Z
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Measures of kurtosis
Kurtosis is measured by β2
β2 = μ4
μ22
Fourth central movement.
Second central movement.
Interpretation-
If β2 > 3 -more peaked than normal( lepto-kurtic)
If β2 < 3 - less peaked than normal( plety-kurtic)
If β2 = 3 – moderate peaked( meso-kurtic)
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2.correlation
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Intro--
it represent the mutual relationship exists between two or
more variables.
eg- relationship b/w price and demand, income and
expenditure, and
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Types of correlation.
1.Positive and negative correlation.
Positive correlation negative correlation
If one variable rises other
also rises and vice- versa.
It two or more variables
move in a same direction.
Eg- relationship b/w price
and supply, sale of pen and
ink.
If one variable rises other
other falls and vice- versa.
It two or more variables
move in a opposite direction.
Eg- relationship b/w price
and demand, investment
and ROI.
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2.Linear and curvi-linear correlation.
LINEAR correlation CURVI-LINEAR correlation
If two variables X and Y
changes in constant ratio.
Every time supply
increases by 20% and its
price rises by 10%.
If two variables X and Y
do not changes in constant
ratio.
Every time supply
increases by 20% and
sometime its price rises by
10% and some time 20%.
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3.simple, partial and multiple correlation.
1.Simple correlation-
When we study the relationship between two variables only.
Relationship bw price and demand, income and consuption.
2.partial correlation-
When two or more variables are taken but relationship b/w any two
of the variables is studied.
Other variable will be constant.
3.Multiple-correlation-
When we study the relationship among three or more variables .
Eg- study of relationship b/w cost of production, output,sale ,advt.
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Degree of correlation.
s.no Degree of correlation Positive Negative
1 Perfect correlation
High degree of correlation.2
Moderate degree of
correlation.
Low degree of correlation.
Absence of correlation.
3
4
5
+1 -1
Between +0.75 to +1 Between -0.75 to -1
Between -0.25 to -
0.75Between +0.25 to
+0.75
Between 0 to +0.25 Between 0 to -0.25
0 0
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Karl Pearson’s coefficient of correlation.
It is quantitative method of measuring correlation.
This method was given by Karl Pearson.
This is the best method of working out correlation
coefficient.
It is denoted as r.
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Properties of the coefficient of correlation.
1.Limits of coefficient of correlation.
Value of Karl Pearson’s correlation coefficient lies b/w -1
and +1.
2.Change of origin and scale
x= 4 +7y
y= 6+8y
Origin
Scale
Shifting the origin or scale not effect the value of
correlation.
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Correlation coeff. Is independent of the change of origin
and scale.
The value of coef. Of corr. B/w two variable x and y and y and x
should be same.
3.Geometric mean of regression coefficient.
r= bxy . byx
4.Symmetric
If the scale of the series is changed or origin is shifted then
corr. Coff. Remain unchanged.
rxy = ryx
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coefficient of determination
The corr. Of deter. Is defined as the square of the
coefficient of correlation.
If the corre. Coeff (r) is 0.8 than coff. Of determinant will
be 0.64 or 64%
Coeff. Of determinant is defined as the ratio of the
expalined variance to the total variance.
r2 = Explained variance
Total variance
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coefficient of non- determination
It is calculated by subtracting the coeff of corr. (r) from 1.
It is denoted as K2
K2 = 1- r2
Coeff. Of non- determinant is defined as the ratio of the
unexpalined variance to the total variance.
K2 = unexplained variance
Total variance
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PREV YEARS QUES.
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Correlation coeff. Is independent of the change of origin
and scale.
The value of coef. Of corr. B/w two variable x and y and y and x
should be same.
3.Geometric mean of regression coefficient.
r= bxy . byx
4.Symmetric
If the scale of the series is changed or origin is shifted then
corr. Coff. Remain unchanged.
rxy = ryx
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SAMPLING &
NON SAMPLINGMETHODS
Statistics Topic-4
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