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

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) (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) (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.)

RELATED QUESTIONS
the mean of a set of six numbers is 2 and the mean of another set of ten numbers is m. if (answered by Boreal)
The arithmetic of set of 50 numbers is 38. If two numbers 45 and 55 are discarded,... (answered by Edwin McCravy)
the mean of a set of numbers is 120. if one number is increased by 300, the mean... (answered by stanbon)
The mean of a set of numbers is 120. If one number is increased by 300, the mean equals... (answered by jrfrunner)
the mean of a set of numbers is 120. if one number is increased by 300, the mean... (answered by neatmath)
the mean of a set of numbers is 120. if one number is increases by 300, the mean... (answered by edjones)
If mean of 100 numbers is 45. The mean that 99 numbers is 44 . What is the first number... (answered by Okeke_Christian)
Problem : The mean of a set of 10 numbers is 67 . If the values 99 and 67 are removed... (answered by ewatrrr)
If the largest number 50 is removed from a set of 10 numbers, the mean is reduced by 4.... (answered by Fombitz)