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
Fresh day Afolayan, let's solve. To find Spearman's rank correlation coefficient, we use the formula: = 1 - (6 d_i^2)/(n(n^2 - 1)) where n is the number of items and d_i is the difference between the ranks of each item. Step 1: List the true ranks (R_i) and observed ranks (S_i) and calculate the differences (d_i = R_i - S_i) and squared differences (d_i^2). The true order (true ranks) is 1, 2, 3, 4. The observed order (observed ranks) is 2, 3, 1, 4. The number of items, n = 4. | Item | True Rank (R_i) | Observed Rank (S_i) | d_i = R_i - S_i | d_i^2 | |------|-------------------|-----------------------|-------------------|---------| | 1 | 1 | 2 | 1 - 2 = -1 | 1 | | 2 | 2 | 3 | 2 - 3 = -1 | 1 | | 3 | 3 | 1 | 3 - 1 = 2 | 4 | | 4 | 4 | 4 | 4 - 4 = 0 | 0 | Step 2: Calculate the sum of the squared differences, d_i^2. d_i^2 = 1 + 1 + 4 + 0 = 6 Step 3: Substitute the values of n and d_i^2 into Spearman's rank correlation coefficient formula. = 1 - (6 × 6)/(4(4^2 - 1)) = 1 - (36)/(4(16 - 1)) = 1 - (36)/(4(15)) = 1 - (36)/(60) Step 4: Simplify the expression to find . = 1 - (3)/(5) = 1 - 0.6 = 0.4 The value of Spearman's rank correlation coefficient is 0.4. Send me the next one 📸