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
To construct a grouped frequency distribution table, we first need to determine the range of the data and the class width. The given data points are: 61, 83, 92, 87, 74, 60, 71, 57, 61, 69 85, 40, 85, 59, 80, 52, 56, 81, 77, 79 73, 82, 43, 64, 67, 48, 18, 68, 37, 43 65, 85, 49, 69, 61, 54, 56, 69, 62, 78 74, 59, 76, 65, 69, 49, 57, 38, 73, 81 Step 1: Find the minimum and maximum values in the data. Minimum value (X_min) = 18 Maximum value (X_max) = 92 Step 2: Calculate the range of the data. Range = X_max - X_min Range = 92 - 18 = 74 Step 3: Calculate the class width. The problem specifies using 6 classes. Class Width (h) = RangeNumber of Classes h = (74)/(6) ≈ 12.33 We round up to a convenient whole number for the class width, so h = 13. Step 4: Define the class intervals. Starting from the minimum value (18) and using a class width of 13: • Class 1: 18 - (18 + 13 - 1) = 18 - 30 • Class 2: 31 - (31 + 13 - 1) = 31 - 43 • Class 3: 44 - (44 + 13 - 1) = 44 - 56 • Class 4: 57 - (57 + 13 - 1) = 57 - 69 • Class 5: 70 - (70 + 13 - 1) = 70 - 82 • Class 6: 83 - (83 + 13 - 1) = 83 - 95 Step 5: Tally the frequency for each class. Let's list the data in ascending order to make tallying easier: 18, 37, 38, 40, 43, 43, 48, 49, 49, 49, 52, 54, 56, 56, 57, 57, 59, 59, 60, 61, 61, 61, 62, 64, 65, 65, 67, 68, 69, 69, 69, 71, 73, 73, 74, 74, 76, 77, 78, 79, 80, 81, 81, 82, 83, 85, 85, 85, 87, 92 • For 18 - 30: 18 (Frequency = 1) • For 31 - 43: 37, 38, 40, 43, 43 (Frequency = 5) • For 44 - 56: 48, 49, 49, 49, 52, 54, 56, 56 (Frequency = 8) • For 57 - 69: 57, 57, 59, 59, 60, 61, 61, 61, 62, 64, 65, 65, 67, 68, 69, 69, 69 (Frequency = 17) • For 70 - 82: 71, 73, 73, 74, 74, 76, 77, 78, 79, 80,