Fundamentals of Mathematical Statistics (BCA) 1st Sem Previous Year Solved Question Paper 2022

To calculate Spearman's rank correlation coefficient for the given data, follow these steps:

Step 1: Rank the data for each subject (Computer and Statistics) separately.

For Computer:
- Rank the Computer scores, ignoring ties but taking the average of the ranks when there are ties.
- Compute the differences between the original student order and the ranked order.
Students | Computer | Rank (Computer) | Difference 
     1                     46                     2                             -1
     2                     65                     4.5                          1.5
     3                     86                      7                              4
     4                     69                       5                             1
     5                     75                       6                             1
     6                     48                       3                            -3
     7                     70                       5                            -2
     8                     68                       4                            -4

For Statistics:
- Rank the Statistics scores, ignoring ties but taking the average of the ranks when there are ties.
- Compute the differences between the original student order and the ranked order.

Students | Statistics  | Rank (Statistics) | Difference 
     1                55                      1                           0
     2                54                    2.5                         0.5
     3                77                     5                            2
     4                75                     4                            0
     5                49                     2                           -3
     6                70                    3.5                        -2.5
     7                70                    3.5                        -3.5
     8                52                     1                            -1

Step 2: Square the "Difference (Computer)" and "Difference (Statistics)" for each student and compute the sum of the squared differences.

Σ(Difference (Computer)²) = (-1)² + (1.5)² + (4)² + (1)² + (1)² + (-3)² + (-2)² + (-4)² = 39.25

Σ(Difference (Statistics)²) = 0² + 0.5² + 2² + 0² + (-3)² + (-2.5)² + (-3.5)² + (-1)² = 28.75

Step 3: Calculate Spearman's rank correlation coefficient (ρ) using the formula:

ρ = 1 - [6 * Σ(Difference (Computer)²) / (n(n² - 1))]
ρ = 1 - [6 * 39.25 / (8(8² - 1))] ≈ 1 - [6 * 39.25 / (8 * 63)] ≈ 1 - 0.36830357 ≈ 0.6317 (rounded to 4 decimal places)

So, Spearman's rank correlation coefficient (ρ) is approximately 0.6317. This indicates a moderate positive correlation between the ranks of Computer and Statistics scores.