मराठी

In the following data one of the value y of is missing. Arithmetic means of x and y series are 6 and 8 respectively. (2=1.4142) x 6 2 10 4 8 y 9 11 ? 8 7 Calculate correlation coefficient - Mathematics and Statistics

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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

बेरीज

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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Concept of Correlation Coefficient
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Correlation - Exercise 5.1 [पृष्ठ ६३]

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