5.9: Modified Boxplots
A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted minimum and maximum values to construct the modified boxplot. The modified minimum value equals the value of Q1 minus the interquartile range multiplied by 1.5. Next, we can calculate the modified maximum value. It is equal to the value of Q3 plus the value of the interquartile range multiplied by 1.5.
Now, the whiskers of the standard box plot are modified. The whiskers are shorter, and the edges of the whiskers lie at the adjusted minimum and maximum values. Further, all the values beyond the modified minimum and maximum values are considered outliers and are marked with an asterisk.