Final answer:
All sets (A, B, C, D) have the same spread of numbers relative to their mean, thus they all have the same standard deviation when considering the relative spread. However, the actual numeric value of the standard deviation is not affected by the multiplication factor, resulting in all sets having the same standard deviation for comparison purposes.
Step-by-step explanation:
The standard deviation is a measure of the spread of data values in a dataset. To determine which set of numbers has the smallest standard deviation, we need to understand that standard deviation is affected by how spread out the numbers are from the mean, not by the actual values themselves. Each of the provided sets (A: 1, 2, 3, 4, 5; B: 10, 20, 30, 40, 50; C: 100, 200, 300, 400, 500; D: 1000, 2000, 3000, 4000, 5000) has the same spread, just multiplied by different factors (1, 10, 100, 1000).
Since the spread of the numbers is the same in all sets, and only the multiplication factor changes, all sets have the same standard deviation when considering their relative spread to the mean. Therefore, the standard deviation of the numbers will be the same for all the sets. However, if we are considering the actual numeric value of the standard deviation, the factor (1, 10, 100, 1000) does not have an impact, because it's the same multiplication factor applied to all numbers in the set, which results in the standard deviation proportionally increasing. Hence, equal spread means equal standard deviation for the purpose of comparison.