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Maths-

General

Easy

Question

Karl Pearson's coefficient of correlation between x and y for the following data is

0.480
– 0.480
0.408
– 0.408

The correct answer is: 0.408

Now, $r equals fraction numerator capital sigma x y minus fraction numerator capital sigma x. capital sigma y over denominator n end fraction over denominator square root of open curly brackets capital sigma x to the power of 2 end exponent minus fraction numerator left parenthesis capital sigma x right parenthesis to the power of 2 end exponent over denominator n end fraction close curly brackets open curly brackets capital sigma y to the power of 2 end exponent minus fraction numerator left parenthesis capital sigma y right parenthesis to the power of 2 end exponent over denominator n end fraction close curly brackets end root end fraction$
Þ $r equals fraction numerator 202 minus fraction numerator 33 cross times 39 over denominator 7 end fraction over denominator square root of open curly brackets 211 minus fraction numerator left parenthesis 33 right parenthesis to the power of 2 end exponent over denominator 7 end fraction close curly brackets open curly brackets 253 minus fraction numerator left parenthesis 39 right parenthesis to the power of 2 end exponent over denominator 7 end fraction close curly brackets end root end fraction$ Þ $r equals 0.408$ .

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