To find out how the range would change by adding the number 5 to the set, we first need to determine the range of the original set of numbers.
The original set is: 5, 4, 7, 3, 9, 2
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First, find the minimum and maximum values in the original set:
- Minimum = 2
- Maximum = 9
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Calculate the range of the original set: \[ \text{Range} = \text{Maximum} - \text{Minimum} = 9 - 2 = 7 \]
Next, we add the number 5 to the set. The new set becomes: 5, 4, 7, 3, 9, 2, 5
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Now find the new minimum and maximum values:
- Minimum = 2 (remains the same)
- Maximum = 9 (remains the same)
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Calculate the new range: \[ \text{New Range} = \text{Maximum} - \text{Minimum} = 9 - 2 = 7 \]
Finally, we determine how much the range has changed: \[ \text{Change in Range} = \text{New Range} - \text{Original Range} = 7 - 7 = 0 \]
Therefore, the range does not increase when the number 5 is added to the set. The answer is: \[ \text{The range increases by } 0. \]