+2 votes
in JEE by kratos

Obtain the rank correlation coeff. For the following data

| X | 68 | 64 | 65 | 50 | 64 | 80 | 75 | 40 | 55 | 64 |
| Y | 62 | 58 | 68 | 45 | 81 | 60 | 68 | 48 | 50 | 70 |

1 Answer

+2 votes
by kratos
 
Best answer

| X | Y | Rank in xi | Rank in yi | d=xi-yi | d2 |
| 68 | 62 | 4 | 5 | -1 | 1 |
| 64 | 58 | 6 | 7 | -1 | 1 |
| 75 | 68 | 2.5 | 3.5 | -1 | 1 |
| 50 | 45 | 9 | 10 | -1 | 1 |
| 64 | 81 | 6 | 1 | 5 | 25 |
| 80 | 60 | 1 | 6 | -5 | 25 |
| 75 | 68 | 2.5 | 3.5 | -1 | 1 |
| 40 | 48 | 10 | 9 | -1 | 1 |
| 55 | 50 | 8 | 8 | 0 | 0 |
| 64 | 70 | 6 | 2 | 4 | 16 |
| Total | | | | | 72 |

In X series 75 is repeated twice which are in the position 2 & 3 in ranks

∴ common rank is 2.5(which is the average of 2&3) is to be given for each 75.Also in X series 64 is repeated 3 times which are in the position 5,6&7 in ranks.

common rank is 5 +6 7/3 = 6 , to be given for each 64

Similarly in Y series 68 is repeated 2 times which are in the position 3&4 in ranks

∴ common rank is 3.5(which is the average of 3&4) is to be given for each 68.

Correction factor

In X series 75 is repeated twice

∴ c.f is 2(22 -1)/12 = 1/2

64 is repeated thrice

∴ c.f is 3(32-1)/12 = 24/12 =2

In Y series 68 is repeated twice

∴ c.f is 2(22 -1)/12 = 1/2

...