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
Welcome back Sabina — missed you this week. To calculate the rank correlation coefficient, we will use Spearman's Rank Correlation Coefficient formula. Step 1: Create a table to calculate the differences in ranks (d) and squared differences (d^2). Let R_A be the rank by students of A and R_B be the rank by students of B. | Method | R_A | R_B | d = R_A - R_B | d^2 | |:------:|:-----:|:-----:|:---------------:|:-----:| | I | 2 | 1 | 2 - 1 = 1 | 1^2 = 1 | | II | 1 | 3 | 1 - 3 = -2 | (-2)^2 = 4 | | III | 3 | 2 | 3 - 2 = 1 | 1^2 = 1 | | IV | 5 | 4 | 5 - 4 = 1 | 1^2 = 1 | | V | 4 | 7 | 4 - 7 = -3 | (-3)^2 = 9 | | VI | 6 | 5 | 6 - 5 = 1 | 1^2 = 1 | | VII | 7 | 6 | 7 - 6 = 1 | 1^2 = 1 | Step 2: Sum the squared differences. d^2 = 1 + 4 + 1 + 1 + 9 + 1 + 1 = 18 Step 3: Identify the number of pairs of observations (n). There are 7 methods, so n = 7. Step 4: Apply Spearman's Rank Correlation Coefficient formula. The formula is: = 1 - (6 d^2)/(n(n^2 - 1)) Substitute the values: = 1 - (6 × 18)/(7(7^2 - 1)) = 1 - (108)/(7(49 - 1)) = 1 - (108)/(7(48)) = 1 - (108)/(336) Simplify the fraction (108)/(336) by dividing both numerator and denominator by their greatest common divisor, which is 12: = 1 - (108 ÷ 12)/(336 ÷ 12) = 1 - (9)/(28) To subtract, find a common denominator: = (28)/(28) - (9)/(28) = (19)/(28) Convert to a decimal: ≈ 0.67857 The rank correlation coefficient is 0.6786. Send me the next one 📸