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Question
Given that r = 0.4 , `Σ(x - barx)(y - bary) = 108 , σ_y = 3 and Σ(x - barx)^2 = 900` . Find the number of pairs of observations.
Solution
`r = ("Cov".(x,y))/(σ_xσ_y)`
r = `((Σ(x - bar x)(y - bar y))/n)/(sqrt((Σ(x - bar x)^2)/n xx σ_y))`
`0.4 = (108/n)/sqrt(900/n xx 3)`
Squaring on both sides
`0.16 = ((108)^2/n^2)/(900/n xx 9)`
∴ `0.16 xx 900 xx 9 = (108 xx 108)/n`
∴ `n = (108 xx 108)/(0.16 xx 900 xx 9)`
∴ n = 9
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