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Question

# n=25,∑x=125,∑x2=650,∑y=100,∑y2=460,∑xy=508. It was observed that two pair of values of (x,y) were copied as (6,14) and (8,6) instead of (8,12),(6,8). The correct correlation coefficient is

A
0.667
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B
0.87
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C
0.25
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D
0.356
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Solution

## The correct option is A 0.667Corrected ∑x=125−6−8+8+6=125Corrected ∑y=100−14−6+12+8=100Corrected ∑x2=650−(6)2−(8)2+(6)2+(8)2=650Corrected ∑y2=460−(14)2−(6)2+(12)2+(8)2=436Corrected ∑xy=508−6×18−8×6+8×12+6×8=520The formula for Pearson product moment correlation isr=n∑xy−(∑x)(∑y)√[n∑x2−(∑x)2][n∑y2−(∑y)2] =25×520−125×100√[25×650−(125)2][25×436−(100)2] =13000−12500√[16250−15625][10900−10000] =500√[625][900] =500(25)(30) =23 =0.667

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