Question

calculate the coefficient of correlation using Karl Pearson's formula of the series given below. X 10 , 12 , 15 , 23 , 20. Y 14 , 17 , 23 , 25 , 21​

Answer 1

Given :

X 10 , 12 , 15 , 23 , 20.

Y 14 , 17 , 23 , 25 , 21​

To find  : the coefficient of correlation using Karl Pearson's formula

Solution:

X 10 , 12 , 15 , 23 , 20

Mean  $\overline{X}$= (10 + 12 + 15 + 23 + 20)/5  = 16

Y 14 , 17 , 23 , 25 , 21​

Mean  $\overline{Y}$= (14 + 17 + 23 + 25 + 21)/5  = 20

X Y X - 16 Y-20 (X - 16)² (Y - 20)² (X-16)(Y-20)

10 14 -6        -6        36                36         36

12 17 -4      -3        16                  9          12

15 23 -1         3          1                  9           -3

23 25 7         5         49                  25           35

20 21 4          1         16                   1           4

                   118                 80         84

r =  ∑ (X  -  $\overline{X}$)(Y -  $\overline{Y}$) / √∑(X  -  $\overline{X}$)²∑(Y  -  $\overline{Y}$)²

=> r = 84 / √(118)80

=> r = 0.8646

coefficient of correlation using Karl Pearson's formula   = 0.8646

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Answer 2

Answer:

calculate the co_efficient using karl person formula of the series given below