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.

candidatesABCDEFGHIJ
Examiner I1st3rd6th2nd10th9th7th4th8th5th
Examiner II2nd1st3rd9th7th4th8th10th5th6th
Examiner III3rd2nd1st6th9th8th7th5th4th10th

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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