Tax reforms committees.
Tax committees and chronological order of taxes. 1.Measures Of Kurtosis Intro--
Like average, dispersion , skewness and Kurtosis is forth measure of frequency distribution.
Kurtosis gives idea about the shape of a frequency distribution. It refer to degree of flatness or peakedness of a frequency curve. Kurtosis indicates whether a frequency distribution is flat, normal and peaked shape. Types of kurtosis 1.Lepto- kurtic It is a curve having high peak than normal curve. Too much concentration the items near the center.
2.Platy-kurtic It is a curve having low peak (flat) than the normal curve. There is less concentration of items near the centre.
3.Meso-kurtic It is a curve having normal peak or the normal curve. There is equal distribution of items around the central value. Lepto-kurtic
Meso-kurtic
platy-kurtic
x̄=M=Z Measures of kurtosis
Kurtosis is measured by β2
μ4 Fourth central movement. β2 = 2 μ2 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) 2.correlation Intro-- it represent the mutual relationship exists between two or more variables. eg- relationship b/w price and demand, income and expenditure, and Types of correlation. 1.Positive and negative correlation.
Positive correlation negative correlation
It two or more variables It two or more variables move in a same direction. move in a opposite direction.
If one variable rises other If one variable rises other also rises and vice- versa. other falls and vice- versa.
Eg- relationship b/w price Eg- relationship b/w price and supply, sale of pen and and demand, investment ink. and ROI. 2.Linear and curvi-linear correlation.
LINEAR correlation CURVI-LINEAR correlation
If two variables X and Y If two variables X and Y changes in constant ratio. do not changes in constant ratio. Every time supply Every time supply increases by 20% and its increases by 20% and price rises by 10%. sometime its price rises by 10% and some time 20%. 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. Degree of correlation.
Degree of correlation s.no Positive Negative
1 Perfect correlation +1 -1
2 High degree of correlation. Between +0.75 to +1 Between -0.75 to -1
3 Moderate degree of Between +0.25 to Between -0.25 to - correlation. +0.75 0.75
4 Low degree of correlation. Between 0 to +0.25 Between 0 to -0.25
5 Absence of correlation. 0 0 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. 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 Origin y= 6+8y Scale Shifting the origin or scale not effect the value of correlation. Correlation coeff. Is independent of the change of origin and scale.
If the scale of the series is changed or origin is shifted then corr. Coff. Remain unchanged.
3.Geometric mean of regression coefficient.
r= bxy . byx
4.Symmetric
The value of coef. Of corr. B/w two variable x and y and y and x should be same.
rxy = ryx 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.
Explained variance r2 = Total variance 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.
unexplained variance K2 = Total variance PREV YEARS QUES.
Correlation coeff. Is independent of the change of origin and scale.
If the scale of the series is changed or origin is shifted then corr. Coff. Remain unchanged.
3.Geometric mean of regression coefficient.
r= bxy . byx
4.Symmetric
The value of coef. Of corr. B/w two variable x and y and y and x should be same.
rxy = ryx
Statistics Topic-4 SAMPLING & NON SAMPLING METHODS