The median of a sample will always equal the midpoint of the data set when the numbers are arranged in order.
To understand this, let’s briefly define what the median is. The median is the value that separates the higher half from the lower half of a data sample. If you have an odd number of observations, the median is the middle number. If there’s an even number of observations, the median is the average of the two middle numbers.
For example, consider the following set of numbers: 3, 1, 9, 7. First, we sort the numbers: 1, 3, 7, 9. Since there are four numbers (an even count), we take the two middle numbers (3 and 7), which results in a median of (3 + 7) / 2 = 5.
This illustrates that the median is not only a measure of central tendency but also a value that lies directly in the center of the data when sorted. Therefore, while the median can represent the general trend of data in a set, it is crucial to remember that its main characteristic is being the value that divides the data set into two equal halves.