b. How is the new standard deviation related to the original standard deviation? A. The standard deviation is multiplied by the absolute value of that constant. B. The absolute value of that constant is added to the standard deviation. C. The standard deviation is divided by the absolute value of that constant. D. The absolute value of that constant is subtracted from the standard deviation

To determine how the new standard deviation is related to the original standard deviation when a constant is applied to a dataset, we need to consider the effects of transformations on standard deviation. 1. **Understanding Standard Deviation**: The standard deviation measures the amount of variation or dispersion in a set of values. 2. **Effect of Multiplying by a Constant**: If each value in a dataset is multiplied by a constant \( k \), the new standard deviation \( \sigma' \) is given by: \[ \sigma' = |k| \cdot \sigma \] where \( \sigma \) is the original standard deviation. This means the standard deviation is scaled by the absolute value of the constant. 3. **Effect of Adding or Subtracting a Constant**: If a constant is added or subtracted from each value in the dataset, the standard deviation remains unchanged. This is because adding or subtracting a constant shifts the entire dataset but does not affect the spread of the data. Based on this understanding, the correct answer to the question is: **A. The standard deviation is multiplied by the absolute value of that constant.**