# Find the number of pairs of observations from the following data, r = 0.15, σy = 4, ∑(xi-x¯)(yi-y¯) = 12, ∑(xi-x¯)2 = 40. - Mathematics and Statistics

Sum

Find the number of pairs of observations from the following data,
r = 0.15, sigma_"y" = 4, sum("x"_"i" - bar"x")("y"_"i" - bar"y") = 12, sum("x"_"i" - bar"x")^2 = 40.

#### Solution

Given, r = 0.15, sigma_"y" = 4, sum("x"_"i" - bar"x")("y"_"i" - bar"y") = 12, sum("x"_"i" - bar"x")^2 = 40

Since, sigma_"x" = sqrt(1/"n" sum("x"_"i" - bar"x")^2) = sqrt(40/"n"

Cov (x, y) = 1/"n" sum("x"_"i" - bar"x")("y"_"i" - bar"y")

= 1/"n" xx 12

∴ Cov (x, y) = 12/"n"

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

∴ 0.15 = (12/"n")/(sqrt(40/"n") xx 4)

∴ 0.15 = 3/("n" xx sqrt(40/"n")

∴ 0.15 = 1/(sqrt("n") xx sqrt(40)
Squaring on both the sides, we get

0.0025 = 1/("n" xx 40)

∴ n = 1/(0.0025 xx 40)

= 10000/(25 xx 40)

= 10000/1000

∴ n = 10

Concept: Concept of Correlation Coefficient
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Chapter 5: Correlation - Miscellaneous Exercise 5 [Page 63]

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