What does the median represent in a data set?

The median represents the middle value in a data set when the numbers are arranged in order from least to greatest. It is a measure of central tendency that indicates the point at which half of the data points fall below and half fall above. This makes the median particularly useful for understanding the distribution of data, especially in cases where the data set may have outliers or skewed values that could distort the average.

In a data set with an odd number of values, the median is simply the middle value, while in a data set with an even number of values, it is calculated as the average of the two central numbers. This characteristic of the median provides a clearer picture of the data set's central point compared to the average, which can be heavily influenced by extreme values. Thus, selecting the median helps to ensure a more robust analysis of data.