Calculate the coefficient of correlation for the following data by the Karl Pearson's actual mean method.
X
Y
12
6
15
8
18
10
21
12
24
14
27 | 30
16 18
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Answered by
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Answer:
Let X denotes price and Y denotes quantity
X
¯¯¯¯¯
X
=
14
(
X
−
¯¯¯¯¯
X
)
2
Y
¯¯¯¯
Y
=
24
(
Y
−
¯¯¯¯
Y
)
2
(
X
−
¯¯¯¯¯
X
)
(
Y
−
¯¯¯¯
Y
)
X
−
¯¯¯¯¯
X
Y
−
¯¯¯¯
Y
10
−
4
16
20
−
4
16
+
16
12
−
2
4
29
+
5
25
−
10
14
0
0
21
−
3
9
0
16
+
2
4
22
−
2
4
−
4
18
+
4
16
28
+
4
16
+
16
∑
X
=
70
∑
(
X
−
¯¯¯¯¯
X
)
∑
(
X
−
¯¯¯¯¯
X
)
2
∑
Y
=
120
∑
(
Y
−
¯¯¯¯
Y
)
∑
(
Y
−
¯¯¯¯
Y
)
2
∑
(
X
−
¯¯¯¯¯
X
)
(
Y
−
¯¯¯¯
Y
)
N
=
5
=
0
=
40
=
0
=
70
=
18
¯¯¯¯¯
X
=
∑
X
N
=
70
5
=
14
;
¯¯¯¯
Y
=
∑
Y
N
=
120
5
=
24
r
=
∑
(
X
−
¯¯¯¯
X
)
(
Y
−
¯¯¯¯
Y
)
√
∑
(
X
−
¯¯¯¯
X
)
2
√
∑
(
Y
−
¯¯¯¯
Y
)
2
=
18
√
40
√
70
=
18
√
2800
=
18
52.91
=
0.34
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