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ii. It is not a quantitative measure of the relationship between the

variables. It is only a quantitative expression of the quantitative
change.
iii. This method is not suitable in case of multiple correlation.

Karl Pearson’s Coefficient of Correlation

Actual Mean Method

Karl Pearson’s Method of measuring coefficient of correlation(r) : -

Prof. Karl-Pearson’s is a British Biometrician Who first advocate the
Product-moment method of measuring coefficient of correlation.

( )
=
×

( − )( − )
 = 2
( − ) 2 × ( − )

 =
2
× 2

where = − = −
Example-1: - From the following data obtain Karl-Pearson’s coefficient of
correlation by using actual mean method.

X 15 18 20 28 34
Y 40 42 46 50 52
Solution: - Karl Pearson’s coefficient of correlation.

2
2

X Y = − = − ×
15 40 -8 -6 64 36 48
18 42 -5 -4 25 16 20
20 46 -3 0 9 0 0
28 50 5 4 25 16 20
34 52 11 6 121 36 66

2
2
=115 =230 =244 =104 =154

= = 115 = 23 = = 230 = 46
5 5

=
2
× 2