A box plot, also known as a box-and-whisker plot, is a graphical representation of statistical data based on the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It is a standardized way of displaying the distribution of data based on a five-number summary. The "box" shows the interquartile range (IQR), which is the range between the first and third quartiles, essentially capturing the middle 50% of the data. The "whiskers" extend from the box to the data's minimum and maximum values, excluding outliers.

Quartiles in a Box Plot

Quartiles are values that divide a data set into quarters:

• First Quartile (Q1): Also known as the lower quartile, it is the median of the lower half of the data set¹.

• Median (Q2): This is the middle value of the dataset when it is ordered from least to greatest. It divides the data set into two equal parts and is also referred to as the second quartile².

• Third Quartile (Q3): Also known as the upper quartile, it is the median of the upper half of the data set¹.

The Interquartile Range (IQR) is the difference between the third and first quartiles (IQR = Q3 - Q1) and represents the central spread of the data. Outliers are typically identified as data points that fall more than 1.5 times the IQR above the third quartile or below the first quartile¹².

Significance of Box Plots

Box plots are particularly useful because they visually show the distribution, central value, and variability of the data. They can also indicate whether the data is skewed and if there are potential outliers. By comparing the lengths of the boxes and the whiskers, one can infer about the spread and skewness of the data. For instance, if the median is closer to the bottom of the box and the lower whisker is shorter, the distribution is positively skewed¹².