Question

Find the karl Pearson’s coefficient of correlation from the following data
and interpret the result.
X: 18 16 14 19
Y: 25 24 22 28​

Answer 1

Answer:

Let the assumed mean for the first variate x be 5 and that for the second variate y be 10.

Here n=9

x y u=x−5 v=y−10 u

2

v

2

uv

1 6 −4 −4 16 16 16

2 5 −3 −5 9 25 15

3 7 −2 −3 4 9 6

4 9 −1 −1 1 1 1

5 8 0 −2 0 4 0

6 10 1 0 1 0 0

7 11 2 1 4 1 2

8 13 3 3 9 9 9

9 12 4 2 16 4 8

∑u=0 ∑v=−9 ∑u

2

=60 ∑v

2

=69 ∑uv=57

ρ(x,y)=

(∑u

2

−

n

(∑u)

2

).

(∑v

2

−

n

(∑v)

2

)

∑uv−

n

1

(∑u)(∑v)

=

(60−

9

(0)

2

)

(60−

9

(−9)

2

)

57−

9

1

(0)(−9)

=

60

60

57

=

60

57

=0.95