Answer and Explanation:
The mean and median cannot be negative. Let’s explore the reasons why.
Mean:
The mean, also known as the average, is calculated by summing up all the numbers in a set and dividing by the total number of values. Since we are only dealing with real numbers in this context, it is not possible for the mean to be negative. When we sum up the numbers, the result will always be a positive or zero value. Dividing this positive or zero value by a positive number will also yield a positive or zero result.
For example, let’s consider the set {1, 2, 3, 4, 5}. The sum of these numbers is 15. Dividing 15 by 5 (the total number of values in the set) gives us a mean of 3. Similarly, if we have a set like {0, 0, 0, 0, 0}, the sum is 0 and dividing by 5 gives us a mean of 0. In both cases, the mean is a non-negative value.
Median:
The median is the middle value in a set of numbers when they are arranged in ascending or descending order. If the set has an odd number of values, the median is the value in the middle. If the set has an even number of values, the median is the average of the two middle values.
Similar to the mean, the median cannot be negative. When we arrange the numbers in ascending or descending order, the median will always be one of the values in the set. Since the values in the set are non-negative, the median will also be non-negative.
For example, let’s consider the set {1, 2, 3, 4, 5}. When arranged in ascending order, the median is 3. If we have a set like {0, 0, 0, 0, 0, 1, 1, 1, 1, 1}, the median is 0.5, which is the average of the two middle values 0 and 1. In both cases, the median is non-negative.
Both the mean and median cannot be negative because they are calculated based on the values in the set, which are non-negative.