To determine the range of a set of numbers, we need to follow a straightforward process. The range is defined as the difference between the maximum and minimum values in a dataset. Let's break this down step-by-step using the numbers provided: 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21, and 16. ### Step 1: Identify the Maximum and Minimum Values 1. **List the Numbers**: - The numbers are: 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21, 16. 2. **Find the Maximum Value**: - The maximum value is the largest number in the list. - Scanning through the numbers, we see that **27** is the largest. 3. **Find the Minimum Value**: - The minimum value is the smallest number in the list. - Looking through the numbers, we find that **3** is the smallest. ### Step 2: Calculate the Range Now that we have identified the maximum and minimum values, we can calculate the range using the formula: \[ \text{Range} = \text{Maximum} - \text{Minimum} \] Substituting the values we found: \[ \text{Range} = 27 - 3 \] Calculating this gives: \[ \text{Range} = 24 \] ### Conclusion The range of the given set of numbers is **24**. Therefore, the correct option is **D. 24**. ### Explanation of Other Options - **Option A: 16**: This is incorrect because it does not represent the difference between the maximum and minimum values. It may be a miscalculation or misunderstanding of the range concept. - **Option B: 21**: This option is also incorrect. It does not reflect the correct calculation of the range. It could be confused with the average or another statistical measure. - **Option C: 23**: This option is incorrect as well. It is one less than the correct range and may arise from a simple arithmetic error in the subtraction step. ### Common Pitfalls - **Misidentifying Maximum or Minimum**: Always double-check to ensure you have correctly identified the largest and smallest numbers. - **Arithmetic Errors**: Be careful with subtraction; it’s easy to make a small mistake that leads to an incorrect range. - **Confusing Range with Other Measures**: Remember that the range is specifically the difference between the maximum and minimum, not the average or median. ### Revision Summary - The range is calculated as the difference between the maximum and minimum values in a dataset. - For the numbers 4, 3, 11, 9, 6, 15, 19, 23, 27, 24, 21, and 16, the maximum is 27 and the minimum is 3. - The range is calculated as \(27 - 3 = 24\). - The correct answer is **D. 24**; other options do not reflect the correct calculation of the range.