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
Here are the solutions for both questions: Question 1: The number of expected classes of a dataset of maximum value of 83 and a minimum value of 11 is .......... Step 1: Calculate the range of the dataset. The range is the difference between the maximum and minimum values. Range = Maximum Value - Minimum Value Range = 83 - 11 = 72 Step 2: Determine the number of classes using the given options and the relationship with class size. The number of classes (k) and class size (w) are related by the formula: k ≈ Rangew. We will check the options for the number of classes to see which one yields a reasonable class size, especially considering the options provided in the second question. If the number of classes is 8 (option a), then the class size would be w = (72)/(8) = 9. This is a common and reasonable class size, and it is also an option in the second question. If the number of classes is 7 (option b), then w = (72)/(7) ≈ 10.29. This is not a whole number and not an option for class size. If the number of classes is 6 (option c), then w = (72)/(6) = 12. This is not an option for class size. If the number of classes is 5 (option d), then w = (72)/(5) = 14.4. This is not a whole number and not an option for class size. Based on this analysis, 8 classes is the most consistent choice. The correct option is a). a. 8 --- Question 12: The class size of a dataset of maximum value of 83 and a minimum value of 11 is ..... Step 1: Calculate the range of the dataset. The range is the difference between the maximum and minimum values. Range = Maximum Value - Minimum Value Range = 83 - 11 = 72 Step 2: Determine the class size using the given options and the relationship with the number of classes. The class size (w) and the number of classes (k) are related by the formula: w ≈ Rangek. We will check the options for the class size to see which one yields a reasonable number of classes, especially considering the options provided in the first question. If the class size is 10 (option a), then the number of classes would be k = (72)/(10) = 7.2. This is not a whole number and not an option for the number of classes. If the class size is 11 (option b), then k = (72)/(11) ≈ 6.55. This is not a whole number and not an option for the number of classes. If the class size is 9 (option c), then k = (72)/(9) = 8. This is a whole number and is an option for the number of classes (option a in the first question). If the class size is 8 (option d), then k = (72)/(8) = 9. This is not an option for the number of classes. Based on this analysis, a class size of 9 is the most consistent choice. The correct option is c). c. 9