Which quartile separates the bottom 50% from the top 50% of a data set?

The quartile that separates the bottom 50% from the top 50% of a data set is the median, also referred to as the second quartile. The median is the middle value when the data is arranged in ascending order. By definition, half of the data points fall below the median and half fall above it, effectively dividing the dataset into two equal parts.

The first quartile (often denoted as Q1) marks the 25th percentile, meaning it is the value below which 25% of the data lies, and the third quartile (Q3) corresponds to the 75th percentile, where 75% of the data falls below that value. Since neither of these quartiles separates the data into two equal halves, they do not serve the purpose described in the question. The second quartile (median) is the only statistical measure that achieves this division.