SOLUTION: The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number

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Question 1195722: The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean = sum / number of elements.
sum = mean * number of elements.
the sum of the first 9 numbers is 9 * 55 = 495
the sum of the 10 numbers is 10 * 56 = 560
the difference = 560 - 495 = 65.
that's the value of the 10th number.
sum of 9 numbers = 495.
the 10th number is 65.
sum of 10 numbers = 495 + 65 = 560.
495/9 = 55
560/10 = 56
this confirms the value of the 10th number is 65.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows a standard method for solving the problem.

Here is a different way that can be useful for many problems like this.

The mean of the 10 numbers is 56.
The mean of the first 9 numbers is 55, so each of those numbers is 1 less than the mean of all 10. So all together the first 9 numbers are a total of 9 below the average of all 10.
That means the 10th number must be 9 MORE than the average of all 10.

ANSWER: the 10th number is 56+9 = 65.

(The 9 above average of the 10th number balances the total of 9 below average of the first 9 numbers.)