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.

Kurtosis indicates whether a frequency distribution

is flat, normal and peaked shape.

It refer to degree of flatness or peakedness of a

frequency curve.

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.

Lepto-kurtic

Meso-kurtic

platy-kurtic

x̄=M=Z

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)

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

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.

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%.

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.

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

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

y= 6+8y

Origin

Scale

Shifting the origin or scale not effect the value of

correlation.

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

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

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

PREV YEARS QUES.

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

SAMPLING &

NON SAMPLINGMETHODS

Statistics Topic-4