Find the Karl Pearson’s coefficient of correlation from
the following data:
x 2 4 4 7 5
y 8 8 5 6 2
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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
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