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Choose four numbers that have the largest possible standard deviation.

A) 1, 2, 3, 4
B) 0, 10, 20, 30
C) -5, 5, -10, 10
D) -50, -25, 25, 50

User Benas
by
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1 Answer

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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.

User Anatoly Alekseev
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