Calculate Spearman's coefficient only

2 Two judges each placed skaters from five countries in rank order. Calculate Spearman's rank correlation coefficient, \(\mathrm { r } _ { \mathbf { s } ^ { \prime } }\) for the two judges' rankings.

2 The orders in which 4 contestants, \(P , Q , R\) and \(S\), were placed in two competitions are shown in the table. Calculate Spearman's rank correlation coefficient between these two orders.

5

1. Write down the value of Spearman's rank correlation coefficent, \(r _ { s }\), for the following sets of ranks. All the discs are replaced in the bag. Tony now takes three discs from the bag at random without replacement.
2. Given that the first disc Tony takes is red, find the probability that the third disc Tony takes is also red.
   [0pt] [2
3. Write down the value of Spearman's rank correlation coefficent, \(r _ { s }\), for the following sets of ranks.
   (b)

   Judge \(A\) ranks	1	2	3	4
   Judge \(C\) ranks	4	3	2	1

   (a)
   (a)

   Judge \(A\) ranks	1	2	3	4
   Judge \(B\) ranks	1	2	3	4

4. Calculate the value of \(r _ { s }\) for the following ranks.

   Judge \(A\) ranks	1	2	3	4
   Judge \(D\) ranks	2	4	1	3

5. For each of parts (i)(a), (i)(b) and (ii), describe in everyday terms the relationship between the two judges' opinions.

Two judges placed 7 dancers in rank order. Both judges placed dancers A and B in the first two places, but in opposite orders. The judges agreed about the ranks for all the other 5 dancers. Calculate the value of Spearman's rank correlation coefficient. [4]