Data set C consists of 12 positive integers less than 70. The list shown gives 11 of the integers from data set C.54,57,56,55,49,50,52,58,51,59,53The mean of these 11 integers is 54. If the mean of data set C is an integer that is greater than 54, what is the value of the largest integer from data set C?
Question
Data set C consists of 12 positive integers less than 70. The list shown gives 11 of the integers from data set C.54,57,56,55,49,50,52,58,51,59,53The mean of these 11 integers is 54. If the mean of data set C is an integer that is greater than 54, what is the value of the largest integer from data set C?
Solution
To solve this problem, we first need to calculate the total sum of the 11 integers given.
The sum of the 11 integers is: 54 + 57 + 56 + 55 + 49 + 50 + 52 + 58 + 51 + 59 + 53 = 594
The mean of these 11 integers is 54, which means the total sum of the 12 integers in data set C is greater than 594.
Since the mean of data set C is an integer greater than 54, the total sum of the 12 integers must be at least 55 * 12 = 660.
Therefore, the 12th integer, which is the largest integer in data set C, must be at least 660 - 594 = 66.
However, the problem states that all integers in data set C are less than 70. Therefore, the largest integer in data set C is 66.
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