# Box Plot Upper Fence is greater than Max

Hi is it normal for the upper fence to be greater than max? If not, what might have gone wrong? I am using Empirical Rule and doing calculation mean +3 * IQR

Thanks

• Perhaps unusual, but not 'illegal'. In quartile-based boxplot, Fences depend on IQR and either Q1 or Q3, but the max or min might be close to Q3 or Q1, respectively. Certainly, if this happens in the upper tail, then there is no outlier in the upper tail. // This can happen easily with samples from short-tailed distn's such as uniform. In R, try code boxplot(runif(20)) several times. Commented May 1, 2022 at 3:26
• Your last sentence doesn't make sense to me. Empirical Rule is not directly related to boxplots. // Technically speaking, Tukey's boxplots use 'fourths'. If boxplot uses quartiles instead of 'fourths', then upper fence is usually Q3 + 1.5(IQR).// Usually, Empirical Rule refers to 'mound shaped' samples which may be nearly normal. // Large normal samples often have a few outliers at each end, so fence outside max in upper tail wouldn't happen. Commented May 1, 2022 at 3:39

• With a small sample from a normal distribution and there will often be no points beyond the fences. With a large sample there will usually be some points beyond the fences, and there is not a good reason to mark them as outliers. The switch seems be around $83-92$ Commented May 1, 2022 at 23:17