# How to Calculate Pearson Correlation Coefficient - Formula, Example

## How to Calculate Pearson Correlation Coefficient - Definition

##### Definition:

Pearson correlation coefficient is a type of correlation coefficient which denotes the relationship between two variables that are measured on the same interval.

##### Formula:
Pearson correlation coefficient ( r ) = Σ [ ( X - My )( Y - Mx ) ] / √ [ ( SSx )( SSy ) ]
###### Where ,

SSx = Σ ( X - Mx ) 2 SSy = Σ ( Y - My ) 2 X = X Values Y = Y Values Mx = Mean of x values My = Mean of y values Σ ( X - Mx ) , Σ ( Y - My ) = Sum of deviation scores Σ ( X - Mx )2 , Σ ( Y - My )2 = Sum of deviation squared

##### Example :

Find the pearson correlation coefficient for this data set.

 x values y values 2 3 4 6 6 4 2 2 5 1
###### Step 1:

Find Mx and My , Mx = [ 2 + 4 + 6 + 2 + 5 ] / 5 Mx = 3.8 My = [ 3 + 6 + 4 + 2 + 1 ] / 5 My = 3.2

###### Step 2:

Then, find the following values,

 ( X - Mx ) ( Y - My ) ( X - Mx )2 ( Y - My )2 ( X - Mx ) * ( Y - My ) -1.8 -0.2 3.24 0.04 0.36 0.2 2.8 0.04 7.84 0.56 2.2 0.8 4.84 0.64 1.76 -1.8 -1.2 3.24 1.44 2.16 1.2 -2.2 1.44 4.84 -2.64 Σ ( X - Mx )=3.6 Σ ( Y - My )=0 Σ ( X - Mx ) 2=12.8 Σ ( Y - My ) 2=14.8 Σ (X - Mx)*(Y - My)=2.2
###### Step 3:

Substitute the given values in the formula = 2.2 / √ [ 12.8 * 14.8 ] = 2.2 / √189.44 = 2.2 / 13.76372 = 0 . 159 Therefore, the pearson correlation coefficient r = 0 . 16