Final answer:
Yes, it is possible for the average of four numbers to be negative even if only one of those numbers is negative. However, that single negative number must be substantial enough to outweigh the combined value of the three positive numbers.
Step-by-step explanation:
If the average of four numbers is negative, it indicates that the sum of those four numbers is negative. Let’s illustrate with the concept of averaging: if you have four numbers a, b, c, and d, their average is calculated by adding these numbers together and then dividing by 4, which can be expressed as (a+b+c+d)/4. For this average to be negative, the sum (a+b+c+d) must also be negative. Now, considering the rules of addition, particularly that when two positive numbers add, the result has a positive sign, and when two negative numbers add, the result has a negative sign, there are different possible combinations of these four numbers.
However, if only one of the four numbers is negative, this single negative number must be large enough in magnitude to outweigh the sum of the three positive numbers to result in a negative sum. This scenario is possible but not guaranteed. It all depends on the magnitudes of the numbers involved. In most cases where large positive numbers are combined with a single smaller negative number, the sum will still be positive. Therefore, although possible, it is not typically likely that three positive numbers and one negative number will average to a negative number unless the negative number is substantially larger in absolute value than the sum of the positive numbers.