How does a box plot use quartiles and the median to display data?

A box plot (or box-and-whisker plot) is a graphical tool that summarizes numerical data by visualizing its distribution, central tendency, and variability. It is constructed using a five-number summary, which includes the minimum value, the first quartile, the median, the third quartile, and the maximum value.123

The plot uses these values as follows:

• The Box: A rectangle is drawn with its ends located at the first quartile ($Q_1$, the 25th percentile) and the third quartile ($Q_3$, the 75th percentile). This box represents the middle 50 percent of the dataset.123
• The Median: A line is drawn inside the rectangle to represent the second quartile ($Q_2$), which is the median or 50th percentile of the data.123
• The Whiskers: Lines extend from the ends of the box to the smallest and largest data values. If outliers are present, the whiskers typically extend only to the range of non-outlier values, with outliers marked as individual points beyond the whiskers.12

This structure allows for a quick assessment of data symmetry, skewness, and the presence of extreme values.1