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Problem: Correlation Coefficient {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} [ Calculator, Method and examples ]

Solution:
Your problem -> Correlation Coefficient {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}}

Mean bar x = (sum x_i)/n

 = (15+25+35+45+55)/5

 = 175/5

 = 35

Mean bar y = (sum y_i)/n

 = (15+25+20+12+8)/5

 = 80/5

 = 16

 Class-X Mid value x y X=(x-35)/10 Y=(y-16)/1 X^2 Y^2 X*Y 10 - 20 15 15 -2 -1 4 1 2 20 - 30 25 25 -1 9 1 81 -9 30 - 40 35 20 0 4 0 16 0 40 - 50 45 12 1 -4 1 16 -4 50 - 60 55 8 2 -8 4 64 -16 --- --- --- --- --- --- --- --- 175 80 sum X=0 sum Y=0 sum X^2=10 sum Y^2=178 sum X*Y=-27

Correlation Coefficient r :
r = (sum XY)/(sqrt(sum X^2) * sqrt(sum Y^2))

=-27/(sqrt(10) * sqrt(178))

=-27/(3.1623 * 13.3417)

=-0.64

Correlation Coefficient r with Population Cov(x,y) :
Population Cov(x,y) = (sum (x-bar x)(y-bar y))/(n)

=-27/5

=-5.4

Population Standard deviation sigma = sqrt((sum (x - bar x)^2)/(n))

=sqrt(10/5)

=sqrt(2)

=1.4142

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