What is the median of a data set?

The median is defined as the middle value of a data set when the values are arranged in ascending or descending order. To find the median, one must first organize the data in order. If the data set has an odd number of observations, the median is simply the middle number. If the data set has an even number of observations, the median is determined by taking the average of the two middle numbers. This concept is essential in statistics as it provides a measure of central tendency that is less affected by extreme values compared to the mean, making it a reliable representation of the data set's center.

This definition distinguishes the median clearly from other statistical measures. For example, the average of all values refers to the mean and is calculated by summing all data points and dividing by the count of these values. The most frequently occurring value is known as the mode, which does not necessarily reflect the central position of the data. The smallest value in the set simply refers to the minimum and does not provide insight into the range or central tendency of the data. Therefore, the definition of the median being the middle value in an ordered data set is accurate and foundational in understanding data distribution.