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For 10 pairs of observations on two variables X and Y, the following data are available - Mathematics and Statistics

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For 10 pairs of observations on two variables X and Y, the following data are available:

`sum(x-2)=30, sum(y-5)=40, sum(x-2)^2=900, sum(y-5)^2=800, sum(x-2)(y-5)=480`

Find the correlation coefficient between X and Y.

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Solution

`sum(x-2)=30, sum(y-5)=40, sum(x-2)^2=900, sum(y-5)^2=800, sum(x-2)(y-5)=480`

Let x – 2 = u and y – 5 = v

`therefore sum u=30, sumv=40, sumu^2=900, sumv^2=800, sumuv=480, m=10`

The correlation coefficient between X and Y.

`=r_(xy)=r_(uv)=(msumuv-sumu sumv)/(sqrt(m sumu^2-1 (sumu)^2)sqrt(m sumv^2-(sumv)^2))`

`=(10xx480-1200)/(sqrt(10xx900-900)xxsqrt(10xx800-1600))`

`=0.5`

Concept: Statistics - Karl Pearson’s Coefficient of Correlation
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