Answer:
r =0.4437
Step-by-step explanation:
We have the follwoing dataset:
X: 20,23,53,4,24,32,35,24,31,23
Y: 30,35,40,38,37,45,50,34,42,32
n=10
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For our case we have this:
n=10 [tex] \sum x = 269, \sum y = 383, \sum xy = 10609, \sum x^2 =8645, \sum y^2 =15007[/tex]
Th excel figure attached shows the calculations for each sum.
[tex]r=\frac{10(10609)-(269)(383)}{\sqrt{[10(8645) -(269)^2][10(15007) -(383)^2]}}=0.4437[/tex]
So then the correlation coefficient would be r =0.4437
