A box plot is a graphical tool to visualize key statistical measures, such as median, mean and quartiles1. The median is the middle value of the data, which divides the data into two equal halves. The variance is a measure of how spread out the data is, calculated as the average squared deviation from the mean. The standard deviation is the square root of the variance, which has the same unit as the data.A box plot can show these three measures by using the following elements2:

The band in the middle of the box indicates the median.

The bottom and top of the box indicate the first and third quartiles, which are the medians of the lower and upper halves of the data. The difference between the third and first quartiles is called the interquartile range (IQR), which is a measure of variability similar to the standard deviation.

The bottom and top of the whiskers represent the minimum and maximum values within 1.5 times the IQR from the first and third quartiles. Any values outside this range are considered outliers and are shown as individual points. The length of the whiskers is related to the variance of the data, as larger variance implies more spread out data and longer whiskers.

The mean is denoted by a small circle, which may or may not be inside the box depending on how skewed the data is. The mean is another measure of central tendency, which is the average value of the data. The distance between the mean and the median reflects the symmetry of the data distribution.

What is a Box Plot?

Box Plot