# 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 - Mathematics and Statistics

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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.

#### 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

Concept: Concept of Correlation Coefficient
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