Solving Bivariate Data Samples

Introduction for bi-variate data samples

The association between the two dissimilar variables is named as bi-variate data set. Those variables are reliant variable and self-governing variable. Reliant variable is a variable, which is depending to the self-governing variable. Self-governing variable is a variable, which is not depending to the reliant variable. Bi-variate data set has several number of numerical pairs, such as` (x_1,y_1), (x_2, y_2),` ..........., `(x_n,y_n)`

The relationship for bi-variate data is found by the following formula,

`r = [Sigma(xy)]/[sqrt([Sigma(x)^2*Sigma(y)^2])]`

These are used in many mathematical approaches such as scatter plot, histogram, distributions, variation etc.

Steps for Bivariate Data Samples Tutor:

  •  Step 1: Find mean for X and Y. These X and Y are the given variables.
  •  Step 2: Find x by subtracting the mean of X from all elements of X.
  •  Step 3: Find y by subtracting the mean of Y from all elements of Y.
  •  Step 4: Multiply x and y.
  •  Step 5: Find [x^2] and [y^2]

 Finally, compute the formula r = `[Sigma (xy)]/[sqrt([Sigma(x)^2 * Sigma(y)^2])]`

Example Problems for Bi-variate Data Samples

Example:

Find the bi-variate relationship for the data.

X

5

10

7

8

5

Y

5

7

4

4

5

 

 

 

Solution:

 

X

Y

x

y

xy

 

 

 

5

5

-2

0

0

4

0

 

10

7

3

2

6

9

4

 

7

4

0

-1

0

0

1

 

8

4

1

-1

-1

1

1

 

5

5

-2

0

0

4

0

Total

35

25

0

0

5

18

6

Mean

7

5

0

0

 

 

 

 

 

 

 

 

 

 

 

 

`r = [Sigma(xy)]/[sqrt([Sigma(x)*Sigma(y)])]`

`r = [5]/[sqrt([18*6])]`

`r = 5/sqrt(108)`

`r = 5/10.39`

`r = 0.48`

Bi-variate relationship value for above table is 0.48

Practice Problems for Bivariate Data Samples

Problem 1:

Solve and obtain bi-variate relationship for given table

X

7

4

8

1

5

Y

6

10

10

9

5

 

 

 

Solution: Bi-variate relationship value for above table is 0.16

Problem 2:

Solve and obtain bi-variate relationship for given table

X

8

2

4

2

4

Y

5

8

7

8

7

 

 

 

Solution: Bi-variate relationship value for above table is 1

Problem 3:

Solve and obtain bi-variate relationship for given table

X

5

2

10

1

7

Y

3

8

9

2

3

 

 

 

Solution: Bi-variate relationship value for above table is 0.4

Problem 4:

Solve and obtain bi-variate relationship for given table

X

9

7

10

9

5

Y

2

10

1

3

4

 

 

 

Solution: Bi-variate relationship value for above table is 1