Question

From the following table, calculate the coefficient of correlation by karl Pearson’s Method: X 6 2 10 4 8 Y 9 11 -- 8 7 Arithmetic means of X and Y series are 6 and 8 respectively

Answer 1

Answer:

Corrected ∑x=125−6−8+8+6=125

Corrected ∑y=100−14−6+12+8=100

Corrected ∑x  

2

=650−(6)  

2

−(8)  

2

+(6)  

2

+(8)  

2

=650

Corrected ∑y  

2

=460−(14)  

2

−(6)  

2

+(12)  

2

+(8)  

2

=436

Corrected ∑xy=508−6×18−8×6+8×12+6×8=520

The formula for Pearson product moment correlation is

r=  

[n∑x  

2

−(∑x)  

2

][n∑y  

2

−(∑y)  

2 ]  

n∑xy−(∑x)(∑y)

​   =  

[25×650−(125)  

2  ]

[25×436−(100)  

2  ]  

25×520−125×100

 =  

[16250−15625][10900−10000]  

13000−12500

 =  

[625][900]  

500

​  =  

(25)(30)

500

​   =  

3

2

 =0.667

Explanation:

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