# 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