Calculate Karl Pearson's coefficient of correlation.

X    18   21   22   19   20   17   20   23   18   22
Y    14   15   18   16   12   13   15   15   17   15

Dear Student
 

X	Y	XY	X2	Y2
18	14	252	324	196
21	15	315	441	225
22	18	396	484	324
19	16	304	361	256
20	12	240	400	144
17	13	221	289	169
20	15	300	400	225
23	15	345	529	225
18	17	306	324	289
22	15	330	484	225

In the table above we have found out X*Y , X² and Y² by using simply multiplication . Then we have recorded the values in the table .
Now we need to add up the columns 
$$\begin{gathered} \sum _{}^{}X= 200 \\ \sum _{}^{}Y=150 \\ \sum _{}^{}XY=2909 \\ \sum _{}^{}{X}^{2^{ }}=4036 \\ \sum _{}^{}{Y}^2=2278 \end{gathered}$$
n = sample size = 10

Therefore , 

Putting the values we get 
r= -910/8.9=-102.2 .

Regards