the arithmetic mean of a set of nine numbers is 5. when one more number is added to the set, the new mean is 5.5. What number was added?
I answered that already.
The total for 9 numbers is 45 and the total for 10 numbers is 55. Take the difference.
(9(5)+x)/10=5.5
45+x=55
x=10
To find the number that was added to the set, we need to calculate the sum of the original set of nine numbers. We know that the arithmetic mean of these numbers is 5 and there are nine numbers in total.
Mean = Sum of numbers / Total number of numbers
Given:
Mean = 5
Number of numbers = 9
Therefore, the sum of the original set of numbers is 5 * 9 = 45.
Now, let's consider the new set of numbers which includes one additional number. We know that the new mean is 5.5.
Mean = Sum of numbers / Total number of numbers
Given:
Mean = 5.5
Number of numbers = 10 (9 original numbers + 1 new number)
Therefore, the sum of the new set of numbers is 5.5 * 10 = 55.
To find the number that was added, we subtract the sum of the original set from the sum of the new set:
55 - 45 = 10
So, the number that was added to the set is 10.
To find the number that was added to the set, we need to first find the sum of the initial nine numbers.
Since the arithmetic mean is the sum of all the numbers divided by the total count, we can write the equation as follows:
(1) Sum of initial nine numbers / 9 = 5
From equation (1), we can conclude that the sum of the initial nine numbers is 45 (since 9 multiplied by 5 equals 45).
Next, we need to find the new sum after adding one more number. Since the new mean is 5.5, we can write the equation as follows:
(2) (Sum of initial nine numbers + New number) / 10 = 5.5
Multiplying both sides of equation (2) by 10, we get:
Sum of initial nine numbers + New number = 55
Substituting the value of the sum of initial nine numbers from equation (1), we get:
45 + New number = 55
Now we can solve for the new number:
New number = 55 - 45 = 10
Therefore, the number that was added to the set is 10.