Calculating Mean After Removing a Number
This problem involves finding the new average (mean) of a set of numbers when one specific number is taken out.
Given Information
- Initial number count: 15
- Initial mean: 25
- Number removed: 36.2
Calculation Steps
-
Calculate the initial sum: The sum of all numbers is the mean multiplied by the count.
Initial Sum = Initial Mean \(\times\) Initial Count
Initial Sum = \(25 \times 15 = 375\)
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Calculate the sum after removal: Subtract the removed number from the initial sum.
New Sum = Initial Sum - Number Removed
New Sum = \(375 - 36.2 = 338.8\)
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Calculate the new count: The count decreases by one after removing a number.
New Count = Initial Count - 1
New Count = \(15 - 1 = 14\)
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Calculate the new mean: Divide the new sum by the new count.
New Mean = New Sum / New Count
New Mean = \(338.8 / 14 \approx 24.2\)
Therefore, the mean of the remaining 14 numbers is approximately 24.2.
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