Question

If the sum of the product of deviations of x and y series from their mean is zero, then the coefficient of correlation will be​

Answer 1

Given : sum of the product of deviations of x and y series from their mean is zero,

To Find :  the coefficient of correlation

Solution:

r = coefficient of correlation

r =  Sxy  / (Sx . Sy)

Correlation coefficient = cov (x,y)/ (std deviation (x) ×std deviation (y))

product of deviations of x and y series from their mean is zero

=> Sxy = 0

=> r = 0

coefficient of correlation  = 0

If the sum of the product of deviations of x and y series from their mean is zero, then the coefficient of correlation will be​  ZERO

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Answer 2

Answer:

To find the the coefficient of correlation

Let r = coefficient of correlation

$r= \frac{Sxy}{Sx.Sy}$

Then Correlation coefficient =  $\frac{cov (x,y)}{(std deviation (x) *std deviation (y))}$

product of deviations of x and y series from their mean is zero =$= > Sxy = 0$

∴$r=0$

∴coefficient of correlation  =$0$

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