To find the range of the original set of numbers, we need to identify the maximum and minimum values in the set:
- The original set is: 4, 8, 2, 6, 6, 3, 6, 3, 8.
- The maximum value is 8.
- The minimum value is 2.
The range is calculated as:
\[ \text{Range} = \text{Maximum} - \text{Minimum} = 8 - 2 = 6. \]
Now, let's consider the new set if we add the number 2:
- The new set will be: 4, 8, 2, 6, 6, 3, 6, 3, 8, 2.
- The maximum value remains 8.
- The minimum value remains 2 (as 2 is already in the set).
The range for the new set is:
\[ \text{New Range} = \text{Maximum} - \text{Minimum} = 8 - 2 = 6. \]
Since both the original range and the new range are 6, the decrease in the range when adding the number 2 is:
\[ \text{Decrease in Range} = \text{Original Range} - \text{New Range} = 6 - 6 = 0. \]
Therefore, the range does not decrease at all.
The answer is that the range decreases by 0.
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