To find the range of a distribution, we need to understand what the range represents. The range is a measure of how spread out the values in a data set are. It is calculated by subtracting the smallest value in the data set from the largest value. ### Step-by-Step Explanation 1. **Identify the Data Set**: The weights of the 10 pupils are: - 15 kg - 16 kg - 17 kg - 18 kg - 16 kg - 17 kg - 17 kg - 17 kg - 18 kg - 16 kg 2. **Find the Maximum Value**: To find the maximum value, we look for the highest weight in the list. - The weights are: 15, 16, 17, 18, 16, 17, 17, 17, 18, 16. - The maximum weight is **18 kg**. 3. **Find the Minimum Value**: Next, we need to find the minimum value, which is the lowest weight in the list. - The minimum weight is **15 kg**. 4. **Calculate the Range**: Now that we have both the maximum and minimum values, we can calculate the range using the formula: \[ \text{Range} = \text{Maximum Value} - \text{Minimum Value} \] Substituting the values we found: \[ \text{Range} = 18 \, \text{kg} - 15 \, \text{kg} = 3 \, \text{kg} \] ### Conclusion The range of the distribution of the weights of the pupils is **3 kg**. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (4)**: This option suggests that the range is 4 kg. However, since the maximum weight is 18 kg and the minimum is 15 kg, the difference is only 3 kg, making this option incorrect. - **Option C (1)**: This option indicates a range of 1 kg. This is incorrect because the difference between the maximum and minimum weights is much larger than 1 kg. - **Option D (2)**: This option suggests a range of 2 kg. Again, this is incorrect as the calculated range is 3 kg, not 2 kg. ### Common Pitfalls - **Misidentifying Maximum and Minimum**: Always double-check to ensure you have correctly identified the maximum and minimum values from the data set. - **Calculation Errors**: Be careful with subtraction; it’s easy to make a mistake when calculating the range if you rush through the arithmetic. ### Revision Summary - The range is calculated as the difference between the maximum and minimum values in a data set. - For the given weights, the maximum is 18 kg and the minimum is 15 kg. - The range is \( 18 \, \text{kg} - 15 \, \text{kg} = 3 \, \text{kg} \). - The correct answer is **B (3)**, as it accurately reflects the calculated range.