Question
The ranks given to twenty branches of a bank on the basis of their deposit mobilisation and recovery of loans, are shown in the following table:
| Deposit Mobilisation |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
| Loan Recovery |
4 |
2 |
9 |
1 |
7 |
10 |
8 |
13 |
5 |
3 |
11 |
6 |
12 |
15 |
14 |
12 |
12 |
14 |
15 |
15 |
Compute the rank correlation coefficient and interpret the result.
Answer :
Word Count : 773
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Skip in 10
We are asked to compute the rank correlation coefficient (Spearman’s ρ) for the ranks of 20 bank branches based on Deposit Mobilisation and Loan Recovery. Let’s solve this step by step manually. --- ### Step 1: Set up the data We have $n = 20$ branches. Let the ranks for Deposit Mobilisation (X) and Loan Recovery (Y) be: | Branch | X | Y | | ------ | -- | -- | | 1 | 1 | 4 | | 2 | 2 | 2 | | 3 | 3 | 9 | | 4 | 4 | 1 | | 5 | 5 | 7 | | 6 | 6 | 10 | | 7 | 7 | 8 | | 8 | 8 | 13 | | 9 | 9 | 5 | | 10 | 10 | 3 | | 11 | 11 | 11 | | 12 | 12 | 6 | | 13 | 13 | 12 | | 14 | 14 | 15 | | 15 | 15 | 14 | | 16 | 16 | 12 | | 17 | 17 | 12 | | 18 | 18 | 14 | | 19 | 19 | 15 | | 20 | 20 | 15 | --- ### Step 2: Compute $d_i = X_i - Y_i$ and $d_i^2$ | Branch | X | Y | d = X-Y | d² | | ------ | -- | -- | ------- | -- | | 1 | 1 | 4 | -3 | 9 | | 2 | 2 | 2 | 0 | 0 | | 3 | 3 | 9 | -6 | 36 | | 4 | 4 | 1 | 3 | 9 | | 5
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