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...

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The question presents a table showing how 10 candidates' essays were ranked by three examiners (I, II, and III). The question requires finding the Spearman's rank correlation coefficient for each pair of examiners to determine which examiners agree most.

(a) The Spearman's rank correlation coefficient measures the strength and direction of the relationship between two variables. It is given by the formula:

r = 1 - (6Σd²)/(n(n²-1))

where d is the difference between the ranks of the two examiners for each candidate, and n is the number of candidates.

(i) To find the correlation coefficient between examiners I and II, we calculate the differences between their ranks for each candidate and square them, then sum the squared differences. Using the formula above, we get r = 0.23, which indicates a weak positive correlation.

(ii) To find the correlation coefficient between examiners I and III, we repeat the same process as above and obtain r = -0.02, which indicates no correlation or a very weak negative correlation.

(iii) To find the correlation coefficient between examiners II and III, we repeat the same process as above and obtain r = 0.23, which indicates a weak positive correlation.

(b) Comparing the correlation coefficients, we can conclude that examiners I and II agree most since they have the highest correlation coefficient of 0.23. However, this correlation is still considered weak.