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Question

The correlation coefficient between xand y from the following data x=40, y=50, xy=220, x2=200, y2=262, n=10is


A

0.89

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B

0.76

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C

0.91

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D

0.98

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Solution

The correct option is C

0.91


Step 1: Finding cov(x,y)

Given x=40,y=50,xy=220, x2=200,y2=262, n=10

We know that cov(x,y)=xyn-x¯.y¯

Let's find the value of x¯,y¯

x¯=xn=4010=4

y¯=yn=5010=5

Substituting the values in the formula, we get

cov(x,y)=22010-(4×5)=22-20=2

Therefore,cov(x,y)=2.

Step 2: Finding the standard deviation

The standard deviation is given by

Sx=x2n-(x¯)2=20010-(4)2=20-16=4=2

Sy=y2n-(y¯)2=26210-(5)2=26.2-25=1.2=1.0954

Step 3: Finding the correlation coefficient

Correlation coefficient of xand y is

r=cov(x,y)Sx.Sy=22×1.0954=0.91

Hence, option (C) is the correct answer


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