09/11/2011
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:
399 comma 456 comma 508 comma 550
Thus, if n is less than or equal to 456, the list of the numbers in increasing order will be
n comma 399 comma 456 comma 508 comma 550 or 399 comma n comma 456 comma 508 comma 550
In either case, the median will be 456. However, if n is greater than 456, the list of numbers in increasing order will be
399 comma 456 comma n comma 508 comma 550
or 399 comma 456 comma 508 comma n comma 550
or 399 comma 456 comma 508 comma 550 comma n
In these cases, the median will be either n or 508. Since you know that the median is 456, it must be true that n is less than or equal to 456. Also, since no two games had the same attendance, the number n cannot be equal to 456. Therefore, the greatest possible value of n is 455.
