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The median of the list of integers is 65.

To find the median, the numbers must first be arranged in ascending order: 62, 65, 80, 92, 96. The median is the middle number, which in this case is 65.

A) 62

Option A is incorrect because 62 is the smallest number in the ordered list and does not represent the middle value. The median must be the central value when the data set is sorted, and 62 does not fulfill that criterion.

B) 65

Option B is correct as 65 is the middle number in the sorted list of integers. With five numbers, the median is the third number, which is indeed 65.

C) 80

Option C is incorrect because 80 is not the middle value in the ordered list. It is the fourth number in the sequence and therefore cannot be the median, which must be the central number.

D) 96

Option D is incorrect as 96 is the largest number in the list and is located at the end of the ordered sequence. The median is defined as the middle value, which 96 does not represent.

E) 92

Option E is also incorrect since 92 is the second highest number in the list. It does not serve as the median, which is specifically the center value of the data set.

Conclusion

The correct answer is 65, as it is the median of the provided integers when arranged in ascending order. All other options fail to represent the middle value, which is crucial for determining the median in a data set. Thus, understanding the concept of median is essential for accurately analyzing sets of numbers.