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Question
Find Karl Pearson's correlation coefficient for the following data :
| X | 3 | 2 | 1 | 5 | 4 |
| Y | 8 | 4 | 10 | 2 | 6 |
Solution
| `X` | `Y` | `X^2` | `Y^2` | `xy` |
| 3 | 8 | 9 | 64 | 24 |
| 2 | 4 | 4 | 16 | 8 |
| 1 | 10 | 1 | 100 | 10 |
| 5 | 2 | 25 | 4 | 10 |
| 4 | 6 | 16 | 36 | 24 |
| 15 | 30 | 55 | 220 | 76 |
Here n =`5,∑x=15,∑y=30,∑x^2=55,∑y^2=220,∑xy=76`
Karl pearson coefficient of correlation between x
and y is
`r(x,y)= (n∑xy-∑x∑y)/(sqrt(n∑x^2-(∑x)^2)sqrt(n∑y^2-(∑y)^2))`
=` (5xx76-15xx30)/(sqrt(5xx55-(15)^2) sqrt(5xx220-(30)^2))`
= `(380-450)/(sqrt(275-225)sqrt(1100-900))`
=`(-70)/(sqrt(50) sqrt(200))`
=`(-70)/100=-0.7`
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