Final answer:
The standard deviation of a data set remains unchanged when a constant is added to or subtracted from each data point in the set. Therefore, if the original standard deviation is 4, it remains 4 after subtracting 2 from each measurement.
Step-by-step explanation:
The question deals with how the standard deviation changes when each measurement in a data set is uniformly adjusted. When you add or subtract a constant from each data point in a set, this translates the data set left or right on the number line but does not affect the spread or variability of the data. Therefore, the standard deviation remains unchanged.
Given that the original standard deviation is 4, after subtracting 2 from each data point, the new standard deviation remains the same, which is 4. The standard deviation is a measure of spread that does not depend on the absolute position of the data set on the number line, but rather on how much the data points differ from their mean value. Since subtracting a constant from each data point does not change these differences, the standard deviation remains the same.