The essays of 10 candidates were ranked by three examiners as shown in the table.
FURTHER MATHEMATICS
WAEC 2020
The essays of 10 candidates were ranked by three examiners as shown in the table.
| candidates | A | B | C | D | E | F | G | H | I | J |
| Examiner I | 1st | 3rd | 6th | 2nd | 10th | 9th | 7th | 4th | 8th | 5th |
| Examiner II | 2nd | 1st | 3rd | 9th | 7th | 4th | 8th | 10th | 5th | 6th |
| Examiner III | 3rd | 2nd | 1st | 6th | 9th | 8th | 7th | 5th | 4th | 10th |
a) Calculate the Spearman's rank correlation coefficient of the ranks assigned by:
(i) Examiners I and lI;
(ii) Examiners I and III
(iii) Examiners II and II.
(b) Using the results in (a), state which two examiners agree most.
Explanation
Rank coefficient = I = \(\frac{6\sum d^2}{n(n^2 - 1)}\)
= 1 - \(\frac{6(141)}{10(10^2 - 1)}\)
= 1 - \(\frac{6(141)}{10 \times 99}\)
= 1 - \(\frac{846}{990}\)
= 1 - 0.85
= 0.15
(ii)
Rank coefficient = 1 - \(\frac{6(78)}{10(10^2 - 1)}\)
= 1 - \(\frac{468}{990}\)
= 1 - 0.472
= 0.53
(iii)
Rank coefficient = 1 - \(\frac{6(78)}{10(10^2 - 1)}\)
= 0.53
(b) Examiner II and III
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