Correlation between {7000, 7500, 6500, 5000, . . . , 12000} & {5200, 5500, 5750, 4300, . . . , 8300}

Workout :

step 1 Address the formula, input parameters and values
data set x = {7000, 7500, 6500, 5000, 7500, 9000, 9500 and 12000}
data set y = {5200, 5500, 5750, 4300, 6000, 8900, 7200 and 8300}
Total number of elements (n) = 8

step 2 Find x̄ & ȳ
x̄ = 64000/8
x̄ = 8000
ȳ = 51150/8
ȳ = 6394

step 3 To find coefficient correlation follow below the table

x	y	X = x - x̄	Y = y - ȳ	X2	Y2	XY
7000	5200	-1000	-1193.75	1000000	1425039.0625	1193750
7500	5500	-500	-893.75	250000	798789.0625	446875
6500	5750	-1500	-643.75	2250000	414414.0625	965625
5000	4300	-3000	-2093.75	9000000	4383789.0625	6281250
7500	6000	-500	-393.75	250000	155039.0625	196875
9000	8900	1000	2506.25	1000000	6281289.0625	2506250
9500	7200	1500	806.25	2250000	650039.0625	1209375
12000	8300	4000	1906.25	16000000	3633789.0625	7625000
∑x = 64000	∑y = 51150	∑X = 0	∑Y = 0	∑X2 = 32000000	∑Y2 = 17742187.5	∑XY = 20425000

step 4 Substitute ∑x, ∑y, ∑xy, ∑x² & ∑y² value in the below correlation coefficient formula

r = ∑XY√∑X². ∑Y²

∑XY = 20425000, ∑X² = 32000000, ∑Y² = 17742187.5

r = 20425000√32000000 x 17742187.5

step 5 Simplify above expression

= 20425000√5.6775E+14

= 2042500023827505.1149

r = 0.8572

Thus 0.8572 is the correlation between x = {7000, 7500, 6500, 5000, 7500, 9000, 9500 and 12000} & y = {5200, 5500, 5750, 4300, 6000, 8900, 7200 and 8300}