This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Assign ranks to the marks in Accountancy (X) and Marks in Statistics (Y). | Marks in Accountancy (X) | Rank (R_X) | Marks in Statistics (Y) | Rank (R_Y) | | :----------------------- | :--------- | :---------------------- | :--------- | | 48 | 5 | 45 | 4 | | 35 | 3 | 20 | 1 | | 17 | 1 | 40 | 3 | | 23 | 2 | 25 | 2 | | 47 | 4 | 48 | 5 | Step 2: Calculate the difference in ranks (d = R_X - R_Y) and the squared difference (d^2). | X | Y | R_X | R_Y | d = R_X - R_Y | d^2 | | :- | :- | :-- | :-- | :-------------- | :---- | | 48 | 45 | 5 | 4 | 1 | 1 | | 35 | 20 | 3 | 1 | 2 | 4 | | 17 | 40 | 1 | 3 | -2 | 4 | | 23 | 25 | 2 | 2 | 0 | 0 | | 47 | 48 | 4 | 5 | -1 | 1 | | | | | | | d^2 = 10 | Step 3: Apply Spearman's rank correlation coefficient formula. The formula for Spearman's rank correlation coefficient () is: = 1 - (6 d^2)/(n(n^2 - 1)) where n is the number of pairs of observations. In this case, n=5. Substitute the values into the formula: = 1 - (6 × 10)/(5(5^2 - 1)) = 1 - (60)/(5(25 - 1)) = 1 - (60)/(5(24)) = 1 - (60)/(120) = 1 - 0.5 = 0.5 The Spearman's rank correlation coefficient is 0.5. Send me the next one 📸