Co Relation 1

7/28/2019 Co Relation 1

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Business Mathematics


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Skewness

X= Md

= Mo

X M

d> M

o

Measures of skewness tell us the direction and the extent of skewness. In symmetrical

distribution the mean, median and mode are identical. The more the mean moves away

from the mode, the large r the asymmetry or skewness.


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Difference between skewness and dispersion

Skewness is the measure of the magnitude as well as direction

of variation in the data.

Dispersion measures only the magnitude of variation.

Symmetrical Frequency Distribution:

Mean=Median=Mode

Asymmetrical Frequency Distribution:

Mode=3(Median)-2(Mean)


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Correlation

When the series of two variables moves in such a way that

changes in one series are accompanied by the fluctuations

in the other, these variables are said to be correlated.

Ex: Increase in the prices of a commodity, reduces its

demand and vice versa.


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Kinds of Correlation

Positive and Negative Correlation

Linear and Non-linear or Curvilinear correlation

Simple, Partial and Multiple Correlation


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Positive and Negative Correlation

When two variables moves in the same direction, ie.

Increase in one variable is associated with the

corresponding increase in other variable, the correlation is

said to be positive.

If when two variables moves in opposite direction or in

other words an increase in one variable is associated with

the corresponding decrease in other or vice-versa, thecorrelation is said to be negative


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Linear and Non-linear or Curvilinear correlation

When the amount of change in one variable tends to bear constant ratio

of change in the other variable, the correlation is said to be linear.

When the amount of change in one variable does not bear a constant

ratio of change in other variable, correlation would be known as

curvilinear (non-linear).


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Linear Positive Correlation Linear Negative Correlation


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Curvilinear Positive Correlation Curvilinear Negative Correlation


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Simple, Partial and Multiple Correlation

Based on no. of variable used

When only two variables are studied, it is a case of simple correlation

coefficient.

When three or more variables are studied simultaneously, it is called

multiple correlation.

Eg. A study of yield per acre of specific type of wheat is studied with a

change in fertilizer and the rainfall- Multiple Correlation

Where as in a partial correlation more than two variables are studied,

but considers the influence of a third variable on the two variables. Theinfluencing variables kept constant. Such problem is known as partial

correlation.


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X 8 10 12 11 9 7 13 14 15 17 16

Y 5 7 9 8 6 4 10 11 12 14 13

Also describe the relationship between X and Y

0

5

10

15

0 5 10 15 20

Y-Values

Y-Values

Draw a scatter diagram for the following data:

Positive correlation between the two variables


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Simple Graphic Method:

Given the following data

X 2 6 8 10 20

Y 16 14 12 8 1

Find the kind of correlation between series X and Y using graphic method

1 2 3 5


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Given the following data:

X 2 6 8 10 20

Y 4 10 12 15 18

Find the kind of correlation between series X and Y using graphic method


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Karl Pearsons Coefficient of Correlation:


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Correlation by Spearmans Rank Method

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