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Question
Two series of x and y with 50 items each have standard deviations of 4.8 and 3.5 respectively. If the sum of products of deviations of x and y series from respective arithmetic means is 420, then find the correlation coefficient between x and y.
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Solution
Given, n = 50, `sigma_"x"` = 4.8, `sigma_"y"` = 3.5, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 420
Cov (x, y) = `1/"n" sum("x"_"i" - bar"x")("y"_"i" - bar"y")`
= `1/50 xx 420`
∴ Cov (x, y) = 8.4
r = `("Cov" ("x", "y"))/(sigma_"x" sigma_"y")`
= `(8.4)/((4.8)(3.5)`
= `(84 xx 10)/(48 xx 35)`
= `1/2`
= 0.5
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