Question

X -68 64 75 50 64 80 75 40 55 64
Y- 62 58 68 45 81 60 68 48 50 70
find out rank correlation between X and Y .​

Answer 1

Given : X -68 64 75 50 64 80 75 40 55 64

Y- 62 58 68 45 81 60 68 48 50 70

To find : rank correlation between X and Y .​

Solution:

X -      68     64    75    50  64   80   75    40   55   64

Rank    7       5      8.5    2      5   10   8.5    1     3     5

Y-      62      58     68    45   81   60    68    48    50   70

Rank  6        4      7.5      1    10    5     7.5       2      3     9

Difference in Ranks

d        1          1         1        1     5    5     1        1         0      4

d²       1         1          1        1    25   25   1        1        0     16

 ∑ (di)² = 72

rank correlation coefficient    = 1   - 6  ∑ (di)² / (n(n² - 1))

n = number of values in group​ = 10

∑ (di)²  = sum of squares of the differences in ranks = 72

rank correlation coefficient  = 1 - 6  * 72/ (10 (10² - 1))

= 1  - 0.43636

0.56364

rank correlation coefficient  0.56364

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