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Find correlation coefficient between x and y series for the following data.

n = 15, `bar"x"` = 25, `bar"y"` = 18, σ_{x }= 3.01, σ_{y} = 3.03, `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122

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#### Solution

here, n = 15, `bar"x"` = 25, `bar"y"` = 18, σ_{x }= 3.01, σ_{y} = 3.03, and `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122

Since, Cov (x, y) = `1/"n" sum_("i"=1)^"n"("x"_"i"-bar"x")("y"_"i"-bar"y")`

∴ Cov (x, y) = `1/15xx122`

= 8.13

Since, r = `("Cov"("x","y"))/(sigma_"x"sigma_"y")`

∴ = `8.13/(3.01 xx 3.03)`

= `8.13/9.1203`

∴ r = 0.89

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