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. Suppose a random sample of earthquakes gave the following information.

x 2.5 4 3.4 4.4 2.4

y 5.2 10.3 10.8 10.3 8.3

Compute r.

a. 0.098

b. -0.013

c. 0.752

d. 0.013

e. -0.752

Answer 1

Solution:

Given that,

x	y	x2	y2	xy
2.5	5.2	6.25	27.04	13
4.0	10.3	16	106.09	41.2
3.4	10.8	11.56	115.64	36.72
4.4	10.3	19.36	106.09	45.32
2.4	8.3	5.76	68.89	19.92
x= 16.7	y= 44.9	x2=58.93	y2 =424.75	xy =156.16

r = n ( xy )- (x ) (y) / n [ ( x² ) - ( x )² ] [ n (y² ) - ( y )²

^r = 5 (156.16) - (16.7 * 44.9⁾ / [ 5 * 58.93 - ( 16.7 ) ²   [ 5 * 424.75 - ( 44.9 ) ² ]

r = 780.8 - 749.83  /  294.65 - 278.89  2123.75 - 2016.01

r = 30.97 /  15.76107.74

r = 30.9 / 3.9699 *10.3798

r = 30.9 / 41.2066

r = 0.7516

= 0.752

Option c ) is correct.