What is the difference between "fliers" and "whiskers" in a boxplot?

Question

Here an example in Python:

In [87]: from pylab import *

In [88]: data = [1,2,3,4,5,6,7,100,101,102]

In [89]: r = boxplot(data)

In [90]: r
Out[90]:
{'boxes': [<matplotlib.lines.Line2D at 0x11b032908>],
 'caps': [<matplotlib.lines.Line2D at 0x11b015390>,
  <matplotlib.lines.Line2D at 0x11b024940>],
 'fliers': [<matplotlib.lines.Line2D at 0x11b062b70>],
 'means': [],
 'medians': [<matplotlib.lines.Line2D at 0x11b062518>],
 'whiskers': [<matplotlib.lines.Line2D at 0x11b0274a8>,
  <matplotlib.lines.Line2D at 0x11b0327b8>]}

I know that the (lower/upper) whiskers are given by Q1 - IQR*1.5 and Q3 + IQR*1.5 (Q1/Q3: 1st/3rd quartile, IQR: interquartile range), and that they are used to identify outliers. But I don't understand what "fliers" are...

According to this SO post, the flier is the line separating outliers, but is that correct?

Answer 1

In traditional boxplot terminology 'fences' are used to determine outliers, but are not plotted. Call the lower quartile $Q_1,$ the upper quartile $Q_3,$ and the interquartile range $IQR = Q_3 - Q_1.$ Then the lower fence is at $Q_1 - 1.5(IQR)$ and the upper fence is at $Q_3 + 1.5(IQR).$

Points below the lower fence or above the upper fence are outliers. The lower whisker goes from $Q_1$ down to the lowest value inside the lower fence. If there is no lower outlier, then it goes down to the minimum. The upper whisker goes from $Q_3$ up to the highest value inside the upper fence. If there is no upper outlier, then it goes up to the maximum. Outliers, if any, are plotted as individual points beyond the ends of whiskers.

I have never heard of 'fliers' before. Maybe that terminology is unique to Python. I looked at the Python code (with which I am not very familiar) and I couldn't distinguish there between 'outlier' and 'flier'.

Some normal data shows outliers. 'Almost all' normal data lies within $\mu \pm 3\sigma,$ but the tails of the distribution go to $\pm \infty,$ so normal data can have far outliers. (I got some moderate outliers on my third try.)

Below is a sample of size 100 generated from $\mathsf{Norm}(100, 15),$ rounded to integers, and sorted. I used R code to show 'boxplot statistics', which include all information needed to draw a boxplot (including 'notched' sides, not used here). I also superimpose dotted red lines to show the locations of the fences. Maybe you can use the same or similar data in Python or read a Python manual to see what is meant by 'fliers.

x = sort(round(rnorm(100, 100, 15)));  x;  boxplot.stats(x)
 [1]  53  60  65  66  72  72  76  78  81  81  81  82  82  82  84  85  86  87  87  89
[21]  89  90  90  90  90  90  91  91  91  92  92  92  92  93  93  93  93  95  95  96
[41]  96  96  96  96  97  97  98  99  99 100 100 101 101 101 101 101 102 102 103 103
[61] 103 104 104 104 105 105 106 106 106 106 106 107 108 109 109 109 110 110 111 112
[81] 112 115 115 118 119 120 120 120 121 122 123 124 124 125 125 127 128 132 132 139

$stats
 [1]  65  90 100 109 132   # 65 and 132 are ends of whiskers

$n
 [1] 100

$conf                      # 'notch' parameter would make CI, not used here
 [1]  96.998 103.002

$out
 [1]  53  60 139

quantile(x)
  0%  25%  50%  75% 100% 
  53   90  100  109  139 
lowr.fence = 90 - 1.5*IQR(x);  lowr.fence
 [1] 61.5
upr.fence = 109 + 1.5*IQR(x);  upr.fence
 [1] 137.5
boxplot(x, pch=19, col="skyblue2")  # 'pch=19' for solid dots
abline(h = c(lowr.fence, upr.fence), col="red", lwd=2, lty="dashed")