Calculate the coefficient of correlation between $x$ and $y$ for the data
x 1 2 3 4 5 6 7 8 9 10
y 3 10 5 1 2 9 4 8 7 6

0.12

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0.19

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0.22

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0.62

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Solution

The correct option is B $0.19$
$x 12345678910_____\sum x = 55$ $y 31051294876_\sum y = 55$ $X = x - ¯ ¯ ¯ x - 4.5 - 3.5 - 2.5 - 1.5 - 0.5 0.5 1.5 2.5 3.5 4.5_0$ $X Y 11.25 - 15.75 1.25 6.75 1.75 1.75 - 1.25 6.25 1.75 2.25_16$ $X^{2} 20.25 12.25 06.25 02.25 00.25 00.25 02.25 06.25 12.25 20.25_82.50$

$Y^{2} 06.25 20.25 00.25 12.25 12.25 02.25 06.25 02.25 00.25___82.50$

Therefore, $¯ ¯ ¯ x = \frac{55}{10} = 5.5$
$\frac{\sum y}{10} = 5.5$

Therefore, $r = \frac{\sum X Y}{\sqrt{\sum X^{2} \sum Y^{2}}} = \frac{16}{82.5} = 0.19$

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Calculate the correlation coefficient between X and Y and comment on their relationship

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X	2	4	5	6	8	11
Y	18	12	10	8	7	5

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