The mean of a group of 10 numbers is 5. If 9 is added into the group what is the new mean?
Understand the Problem
The question asks to calculate the new mean after adding a number to an existing group of numbers, given the original mean and number of elements. We will first find the sum of the original 10 numbers, then add the new number (9) to that sum, and finally divide by the new count (11) to find the new mean.
Answer
12.1
Answer for screen readers
12.1
Steps to Solve
- Find the sum of the original 10 numbers
We know the original mean of 10 numbers is 12.4. The mean is calculated by dividing the sum of the numbers by the count of the numbers. Therefore, we can find the sum by multiplying the mean by the count.
$$ \text{Sum} = \text{Mean} \times \text{Count} $$
$$ \text{Sum} = 12.4 \times 10 = 124 $$
- Add the new number to the sum
We are adding the number 9 to the original sum.
$$ \text{New Sum} = \text{Original Sum} + \text{New Number} $$
$$ \text{New Sum} = 124 + 9 = 133 $$
- Calculate the new mean
Now, we need to divide the new sum by the new count, which is 11 (the original 10 numbers plus the new number).
$$ \text{New Mean} = \frac{\text{New Sum}}{\text{New Count}} $$
$$ \text{New Mean} = \frac{133}{11} = 12.090909... $$
- Round to one decimal place
Rounding the new mean to one decimal place, we get 12.1
12.1
More Information
The new mean after adding 9 to the original set of numbers and rounding to one decimal place is 12.1.
Tips
A common mistake is forgetting to add the new number to the sum of the original numbers, instead of just averaging 9 with 12.4. Another mistake is not increasing the total count of numbers to 11 when calculating the new mean. Finally, not rounding to the specified number of decimal places is a common error.
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