In statistics, what does the term 'median' refer to?

The median is defined as the middle value in a dataset when the values are arranged in ascending or descending order. This means that if the dataset has an odd number of observations, the median is the single middle number. If the dataset has an even number of observations, the median is calculated by taking the average of the two middle numbers.

For example, in the dataset {3, 1, 4, 2, 5}, when arranged in order, the numbers are {1, 2, 3, 4, 5}. The median would be 3, as it is the middle value. In a dataset like {1, 2, 3, 4}, there are two middle numbers (2 and 3), so the median would be (2 + 3) / 2 = 2.5.

This characteristic of the median makes it a robust measure of central tendency, especially in datasets that may have outliers or extreme values, which can skew the average. Thus, the median serves as a valuable statistic that provides insight into the central location of the data without being influenced heavily by those extreme values.