What does the third quartile in a data set represent?

The third quartile, often denoted as Q3, is a measure of statistical dispersion that represents the value below which 75% of the data falls. This means that if you were to arrange a data set in increasing order, the third quartile would be at the 75th percentile. Consequently, it effectively acts as the boundary between the lower 75% and the upper 25% of the data.

In terms of its relationship to the median, the third quartile is specifically the median of the upper half of the data. Since 50% of the data lies below Q2 (the median), and Q3 marks the point where 75% of the data has been accounted for, it is accurate to say that Q3 represents the median of the top 50% of the data set. Understanding this allows for a better grasp of how data is distributed, particularly in identifying outliers and understanding the spread of the upper portion of a data set.