Question

If a distribution is said to be symmetric, which of the following statements would be true? The mean will be larger than the median. The mean will be equal to the median. The mean will be smaller than the median. We do not have sufficient information to identify the relationship between the mean and the median.

Answer 1

Explanation:

If a distribution is said to be symmetric, it means that the shape of the distribution is balanced and mirror-image on both sides of its center. In other words, the left and right sides of the distribution are roughly equal.

In a symmetric distribution, the mean and median will be equal. This is because the mean is the average of all the values in the distribution, and the median is the middle value when the values are arranged in ascending or descending order. Since the distribution is symmetric, the middle value will be the same as the average of all the values.

For example, let's say we have a distribution of exam scores: 70, 75, 80, 85, 90. If we calculate the mean, we add up all the values (70+75+80+85+90) and divide by the total number of values (5). The mean is 80.

To find the median, we arrange the values in ascending order: 70, 75, 80, 85, 90. The middle value is 80, which is the same as the mean.

Therefore, if a distribution is symmetric, the mean will be equal to the median.