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3 Responses
Different conventions exist; a common textbook choice is Tukey’s method (hinges) for quartiles and “adjacent values” for whiskers: take Q1 and Q3 as the medians of the lower and upper halves (excluding the overall median), and extend whiskers to the most extreme points within 1.5×IQR. Example: for 1,2,3,6,7,10 we get Q1=2, median=4.5, Q3=7, IQR=5, fences −5.5 to 14.5, so the whiskers reach 1 and 10; see https://www.khanacademy.org/math/statistics-probability/displaying-describing-data/box-plots/a/constructing-a-box-plot.
I’d use Tukey’s rule: split at the median and take Q1, Q3 as the medians of 1,2,3 and 6,7,10, giving Q1=2, Q3=7 (IQR=5). The whiskers then extend to the most extreme points within 1.5·IQR, so here they should reach 1 and 10-if a whisker stops at 2, the book is using a different convention or it’s a slip.
I’d use the “exclusive-median” rule: take Q1 and Q3 as the medians of the lower and upper halves (2 and 7), then draw whiskers only to the nearest data outside each quartile rather than all the way to min/max-so for 1,2,3,6,7,10 you get Q1=2, Q3=7, IQR=5, lower whisker at 2 (shy!) and upper whisker at 10.