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Question : Calculate rank correlation coefficient of the Following ranks obtained by 10 students in two subjects, statistics and mathematics.
| Statistics | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mathematics | 2 | 4 | 1 | 5 | 3 | 9 | 7 | 10 | 6 | 8 |
Answer :
Rank Correlation Coefficient is calculated by the following formula
\[\rho\ =1-\frac{6\sum D^2}{N\left(N^2-1\right)}\]
Where D is difference of ranks and N is number of paired data.
| Ranks in Statistics ( x) | Ranks in Mathematics (y) | D=x-y | D^2 |
| 1 | 2 | -1 | 1 |
| 2 | 4 | -2 | 4 |
| 3 | 1 | 2 | 4 |
| 4 | 5 | -1 | 1 |
| 5 | 3 | 2 | 4 |
| 6 | 9 | -3 | 9 |
| 7 | 7 | 0 | 0 |
| 8 | 10 | -2 | 4 |
| 9 | 6 | 3 | 9 |
| 10 | 8 | 2 | 4 |
| Sum=40 |
Therefore
Therefore \[\rho\ =1-\frac{6\ast40}{10\left({10}^2-1\right)}=1-\frac{240}{990}=\frac{990-240}{990}=\frac{750}{990}=\frac{75}{99} \] \[\rho=0.7576\]
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