Write out the numbers of the "X" and "Y" values you want the correlation coefficient of:
X Values Y Values
20 4.1
21 4.6
Count the total number of "X" and "Y" values; in this case, there are four, so "N"=4.
Multiply "X" by "Y," "X" by "X" and "Y" by "Y" for all four values with a calculator:
X*Y=20*4.1=82 X*Y=21*4.6=96.6
X*X=20*20=400 X*X=21*21=441
Y*Y=4.1*4.1=16.81 Y*Y=4.6*4.6=21.16
Add up the "X" values, the "Y" values and all of the multiplied "X" and "Y" values; find the square roots of the "X" and "Y" values and add them together:
X+X=20+21=41
Y+Y=4.1+4.6=8.7
X*Y=20*4.1=82 and X*Y=21*4.6=96.6 and 82+96.6=178.6
X*X=20*20=400 and X*X=21*21=441 and 400+441=841
Y*Y=4.1*4.1=16.81 and Y*Y=4.6*4.6=21.16 and 16.81+21.16=37.97
Plug the numbers into the formula (r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX^2 - (ΣX)^2][NΣY^2 - (ΣY)^2])] and make the calculations with the calculator:
Correlation(r)=((4)*(178.6)-(41)*(8.7)) / square-root ([4)*(841)-(41*41)]*[(4)*(37.97)-(8.7*8.7)])
Correlation(r)=(714.4-356.7) / square-root ([3364-1681)*[151.88-75.69)
Correlation(r)=357.7 / square-root (1683*76.19)
Correlation(r)=357.7 / square-root (128227.77)
Correlation(r)=357.7 / 358.089
Correlation(r)=0.9989