What does the median represent in a data set?

The median represents the middle number when a data set is arranged in order. This measure of central tendency effectively divides a dataset into two equal halves, where half of the values lie below it and half are above it. It is particularly useful in situations where the data set may contain outliers or extreme values, as the median is less influenced by these than the mean, thus providing a better representation of the central position of the data.

For example, in a dataset like {3, 5, 7, 15, 100}, the median would be 7, which accurately reflects the center of the main body of data, unlike the mean, which would be skewed higher due to the outlier value of 100. The median's strength lies in its ability to provide a clear and robust measure of central tendency that is often utilized in psychological research for understanding distributions and interpreting scores.