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Maths-

General

Easy

Question

Karl Pearson's coefficient of correlation between the heights (in inches) of teachers and students corresponding to the given data is

$\frac{1}{\sqrt{2}}$
$\sqrt{2}$
$- \frac{1}{\sqrt{2}}$
0

The correct answer is: $fraction numerator 1 over denominator square root of 2 end fraction$

Here $capital sigma left parenthesis x minus stack x with ̄ on top right parenthesis left parenthesis y minus stack y with ̄ on top right parenthesis equals 10 comma capital sigma left parenthesis x minus stack x with ̄ on top right parenthesis to the power of 2 end exponent equals 10$
and $capital sigma left parenthesis y minus stack y with ̄ on top right parenthesis to the power of 2 end exponent equals 20$
Hence the coefficient of correlation is given by
$r equals fraction numerator capital sigma left parenthesis x minus stack x with ̄ on top right parenthesis left parenthesis y minus stack y with ̄ on top right parenthesis over denominator square root of capital sigma left parenthesis x minus stack x with ̄ on top right parenthesis to the power of 2 end exponent capital sigma left parenthesis y minus stack y with ̄ on top right parenthesis to the power of 2 end exponent end root end fraction equals fraction numerator 10 over denominator square root of 10 cross times 20 end root end fraction equals fraction numerator 10 over denominator 10 square root of 2 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction$ .

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