Final answer:
The arithmetic mean of all integers x such that −80 < x < 80 is 0.5.
Step-by-step explanation:
The arithmetic mean, or average, of a set of numbers is found by summing all the numbers and dividing by the count of numbers. In this case, we are looking for the arithmetic mean of all the integers x such that −80 < x < 80. To find the mean, we add up all the integers within this range and divide by the count of numbers, which is 159. Therefore, the arithmetic mean is 0.5.