Calculate the rank-coefficient of correlation from the following data :
X 80 78 75 75 68 67 60 59
y 12 13 14 14 14 16 15 17
Answers
Explanation:
Given Calculate the rank-coefficient of correlation from the following
data :X 80 78 75 75 68 67 60 59
y 12 13 14 14 14 16 15 17
- So we need to find rank coefficient. So we have
X Y R1 R2 R1 – R2 D^2
80 12 1 8 - 7 49
78 13 2 7 - 5 25
75 14 3.5 5 - 1.5 2.25
75 14 3.5 5 - 1.5 2.25
58 14 8 5 3 9
67 16 5 2 3 9
60 15 6 3 3 9
59 17 7 1 6 36
- Total 141.5
- So ∑ D^2 = 141.5
- here the value 75 is repeated twice the rank will be taken as 3rd and 4th respectively, and so it will be 3 + 4 / 2 = 7/2 = 3.5
- In the same way 14 is also repeated thrice and the rank is taken as 4,5 and 6 respectively and so it will be 4 + 5 + 6 / 3 = 15/3 = 5
- Since 75 is repeated twice and 14 is repeated thrice m1 = 2 and m2 = 3
- So r = 1 - 6 [ ∑D^2 + 1/12 (m1^3 – m1) + 1/12 (m2^3 – m2) / n^3 - n
- = 1 - 6 [ 141.5 + 1/12 (2^3 – 2) + 1/12 (3^3 – 3)] / 8^3 – 8 (since n is number of terms)
- = 1 – 6 x 144 / 504
- = 1 – 12 / 7
- = - 5 / 7
- = - 0.71428
Reference link will be
https://brainly.in/question/12434925