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Mathematics > Standard Multiple Choice

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The table above shows the attendance at the home games of the Central High School football team. If the median attendance for the five games was , and no two games had the same attendance, what is the greatest possible value for ?

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### Explanation

The median of five numbers can be found by putting the numbers in increasing order and picking the middle, or third, number from the list. Putting the four numbers you know in increasing order produces the following list:

Thus, if is less than or equal to , the list of the numbers in increasing order will be

or

In either case, the median will be . However, if is greater than , the list of numbers in increasing order will be

or

or

In these cases, the median will be either or . Since you know that the median is , it must be true that is less than or equal to . Also, since no two games had the same attendance, the number cannot be equal to . Therefore, the greatest possible value of is .

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