How is the median defined?

The median is defined as the middle value of a data set when it is arranged in ascending order. This means that to find the median, you first organize the data points from the smallest to the largest. If the data set has an odd number of observations, the median is simply the value that lies right in the center. However, if there is an even number of observations, the median is calculated by taking the average of the two middle values. This characteristic of the median makes it a robust measure of central tendency, particularly because it is not affected by extreme values or outliers, providing a better representation of the center of the data in such cases.

Other definitions in the options do not accurately describe the median. For instance, stating that the median is the mode relates to a different statistical concept, which refers to the most frequently occurring value in the data set. Describing the median as an average refers to the mean, which is calculated by summing all the values and dividing by the number of values, rather than focusing on the positional central tendency. Lastly, calling the median the maximum value misunderstands its definition, as the maximum represents the largest single value in the data, not a measure of central tendency.