Final answer:
The set of numbers that has the largest possible standard deviation is -50, -25, 25, 50, since it has the largest range which indicates a greater spread of values.
Step-by-step explanation:
To determine which set of four numbers has the largest possible standard deviation, we need to look for the set with the greatest spread, as standard deviation is a measure of how spread out the numbers are from their mean.
- A) 1, 2, 3, 4
- B) 0, 10, 20, 30
- C) -5, 5, -10, 10
- D) -50, -25, 25, 50
Now, we compare the ranges of these sets, since the range is connected to standard deviation:
- A) The range is 4 - 1 = 3
- B) The range is 30 - 0 = 30
- C) The range is 10 - (-10) = 20
- D) The range is 50 - (-50) = 100
Set D has the largest range, indicating that the numbers are more spread out compared to the other sets. Thus, set D will have the largest standard deviation.