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
Boxplot – How to Interpret Box Plot Upper Fence Greater Than Max
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Related Solutions
You just calculated the limits on where the whiskers can go, not the whisker ends themselves (which are limited to the range of the data).
The actual whiskers go out to the furthest-out data value inside the (inner) fences. The fences can go outside the data, but aren't actually plotted.
(for more details see this image, which is from this page)
R's boxplot function, by default, uses boxplot.stats to calculate the boxes, whiskers, etc... boxplot.stats calls the fivenum function:
> fivenum(c(0.734522222, 0.939425))
[1] 0.7345222 0.7345222 0.8369736 0.9394250 0.9394250
According to ?fivenum:
Tukey's five number summary (minimum, lower-hinge, median, upper-hinge, maximum)
The minimum and lower-hinge are identical. Similarly, the upper-hinge and maximum are identical.
Best Answer
Yes, it is fairly normal for the upper fence to be greater than the maximum. That's the point of the fences -- with a Normal or light-tailed distribution, there will often be no points beyond the fences. Any that are beyond the fences get marked as outliers.
Note that (according to Tukey) the end of the whisker of the boxplot shouldn't be the fence, it should be the last observation before the fence