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प्रश्न
In the following data one of the value y of is missing. Arithmetic means of x and y series are 6 and 8 respectively. `(sqrt(2) = 1.4142)`
| x | 6 | 2 | 10 | 4 | 8 |
| y | 9 | 11 | ? | 8 | 7 |
Calculate the correlation coefficient
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उत्तर
We construct the following table:
| x | y | x2 | y2 | xy | |
| 6 | 9 | 36 | 81 | 54 | |
| 2 | 11 | 4 | 121 | 22 | |
| 10 | 5 | 100 | 25 | 50 | |
| 4 | 8 | 16 | 64 | 32 | |
| 8 | 7 | 64 | 49 | 56 | |
| Total | 30 | 40 | 220 | 340 | 214 |
Here, `sum_"x" = 30, sum_"y" = 40`
`sum"x"^2 = 220; sum"y"^2 = 340`
`sum"xy" = 214`; n = 5
∴ Karl Pearson’s coefficient of correlation,
r = `("n"sum"xy" - sum"x" sum"y")/(sqrt("n" sum"x"^2 - (sum"x")^2) sqrt("n" sum"y"^2 - (sum"y")^2)`
= `(5(214) - 30(40))/(sqrt(5(220) - (30)^2)sqrt(5(340) - (40)^2)`
= `(-130)/(sqrt(200) sqrt(100)`
∴ = – 0.92
∴ There is high degree negative correlation.
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