Question

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. x 2.5 4.1 3.3 4.5 2.6 3.2 3.4 y 4.8 10.3 11.2 10.0 7.9 3.9 5.5

Answer 1

Yes, the magnitude of earthquake tends to increase with the increase in depth, and vice versa.

Explanation:

Step 1:

Make a scatter plot from the values:

(Attachment)

Step 2:

Find Correlation Coefficient 'r'

Using calculator, first find

∑x= 2.5+4.1+3.3+4.5+2.6+3.2+3.4 = 23.6

∑y= 4.8+10.3+11.2+10.0+7.9+3.9+5.5 = 53.6

∑x²= (2.5)²+(4.1)²+(3.3)²+(4.5)²+(2.6)²+(3.2)²+(3.4)² = 82.76

∑y²=(4.8)²+(10.3)²+(11.2)²+(10.0)²+(7.9)²+(3.9)²+(5.5)² =462.44

∑xy = (2.5*4.8)+(4.1*10.3)+(3.3*11.2)+(4.5*10.0)+(2.6*7.9)+(3.2*3.9)+(3.4*5.5) = 187.91

n=7

Substitute all in the formula of Correlation Coefficient

r=0.5587

As the value is positive, it means that when x increase, y also tends to increase,and vice versa