To determine how many minutes of TV Micah could have watched in order to increase the range, we first need to calculate the initial range of Luke's data.
The current data points are: 45, 120, 90, 90, 180, 110.
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Calculate the minimum and maximum values:
- Minimum (min) = 45
- Maximum (max) = 180
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Calculate the current range:
- Range = max - min = 180 - 45 = 135
To increase the range after adding Micah's data point, we have a couple of scenarios:
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If Micah watches more than the current maximum (180):
For example, if Micah watches 181 minutes, the new maximum would be 181, and the new range would be:- New range = 181 - 45 = 136 (which is greater than 135).
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If Micah watches less than the current minimum (45):
For example, if Micah watches 44 minutes, the new minimum would be 44, and the new range would be:- New range = 180 - 44 = 136 (also greater than 135).
Thus, Micah can either watch more than 180 minutes or fewer than 45 minutes to increase the range. Therefore, Micah could watch:
- Any amount greater than 180 minutes (e.g., 181, 200, etc.) or
- Any amount less than 45 minutes (e.g., 44, 30, etc.).
These scenarios will ensure that the range increases.
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