Rank correlation coefficient, also known as Spearman's rank correlation coefficient, is used to measure the strength and direction of the relationship between two sets of ranked data. In this case, we are given the ranks of students in two subjects, A and B. To find the rank correlation coefficient, we need to follow these steps:

Step 1: Calculate the difference between the ranks of each student in both subjects.
Step 2: Square the differences obtained in Step 1.
Step 3: Calculate the sum of squared differences.
Step 4: Use the formula to calculate the rank correlation coefficient.

Let's calculate the rank correlation coefficient for the given data:

Step 1: Calculate the difference between the ranks of each student in both subjects.

Student Name Rank in A Rank in B Difference (d)
1 3 5 -2
2 4 7 -3
3 1 1 0
4 2 4 -2
5 5 3 2
6 7 2 5
7 9 8 1
8 8 9 -1
9 6 6 0

Step 2: Square the differences obtained in Step 1.

Student Name Rank in A Rank in B Difference (d) Squared Difference (d^2)
1 3 5 -2 4
2 4 7 -3 9
3 1 1 0 0
4 2 4 -2 4
5 5 3 2 4
6 7 2 5 25
7 9 8 1 1
8 8 9 -1 1
9 6 6 0 0

Step 3: Calculate the sum of squared differences.

Sum of squared differences (Σd^2) = 4 + 9 + 0 + 4 + 4 + 25 + 1 + 1 + 0 = 48

Step 4: Use the formula to calculate the rank correlation coefficient.

Rank correlation coefficient (ρ) = 1 - (6Σd^2) / (n(n^2-1))
where n is the number of observations.

In this case, n = 9.

Rank correlation coefficient (ρ) = 1 - (6 * 48) / (9 * (9^2-1))
= 1 - (288) / (9 * 80)
= 1 - 32 / 80
= 1 - 0.4
= 0.6

Therefore, the rank correlation coefficient for the given data is 0.6, indicating a moderate positive relationship between the ranks in subjects A and B.