What does the first quartile represent in a box plot?

The first quartile, often denoted as Q1, represents the median of the lower half of a data set in a box plot. This means that it is the value separating the lowest 25% of the data from the rest. To find the first quartile, you would first organize all the data points in ascending order and then identify the median of the values that are below the overall median.

This concept is important in understanding the distribution of data, as quartiles (including Q1, Q2, which is the median, and Q3, which is the third quartile) divide the data set into four equal parts. The first quartile gives insight into the lower range of the data set, allowing for a better understanding of its spread and central tendency.