To find the increase in the mean when the number 5 is added to the set of numbers, we first calculate the mean of the original set.
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Calculate the mean of the original set of numbers:
- The original set is just one number: 783174.
- To find the mean, we sum the numbers and then divide by the quantity of numbers. \[ \text{Mean} = \frac{783174}{1} = 783174 \]
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Add the number 5 to the set:
- Now, the new set of numbers is {783174, 5}.
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Recalculate the mean of the new set:
- The sum of the new set is: \[ 783174 + 5 = 783179 \]
- There are now 2 numbers in the new set. \[ \text{New Mean} = \frac{783179}{2} = 391589.5 \]
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Determine the increase in the mean:
- The increase in the mean is calculated by subtracting the original mean from the new mean: \[ \text{Increase} = 391589.5 - 783174 \]
- This will actually show how the mean has changed: \[ \text{Increase} = 391589.5 - 783174 = -391584.5 \]
However, since we actually meant how much the mean itself changes by adding 5, we realize that the mean has decreased significantly.
- Final answer:
- The mean increases in value in relation to how we initially perceived it as high based on the sum compared to the change, but it actually decreases overall due to the ratio.
Thus, the mean decreases with the addition of 5, making this an interesting exercise in understanding means and sums.
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