# Interpreting percentage of an outlier in a box plot

I have a dataset of 21 points. Below is a box plot of that data.

I am trying to interpret this boxplot. Is it safe to say that 96% of my data points fall under 48? I derived 96% by dividing 100 with 21 (length of my dataset). I am assuming it is not correct to say 100% of the data is below 48 because of the outlier.

UPDATE

I am not looking for an explanation on what box plots are. I understand what they help identify and interpret. I understand IQR's, percentiles, range etc. I have added additional details to the title of my question to provide more clarity.

• Possible duplicate of How to interpret a box plot? Jan 24, 2019 at 2:35
• @Stefan I have updated my question. Jan 24, 2019 at 2:54
• You need to research how this plot was constructed. Most boxplots would extend their whiskers up to 3/2 times the box height, but stop at the most extreme value within those "fences." That suggests the whiskers both terminate at data values. This would place at most 19 of the data values below 48 and (because the box and everything below it contains at least 15 values) at least 15 values would lie below 48. That's all one can reliably determine from the plot, although it's likely the top dot represents just one value and possibly there's only one value at the tip of the upper whisker.
– whuber
Jan 24, 2019 at 15:44
• @whuber Can you explain why you this part of your comment - at least 15 values would lie below 48 Jan 24, 2019 at 19:19
• The box itself comprises the middle 10 to 12 observations (depending on how it is computed; as originally defined by John Tukey, it would include at least 11). The region below the box comprises the lowest 5 (or perhaps 6) observations. All these are plotted at heights below 48.
– whuber
Jan 24, 2019 at 20:29

You don't need a boxplot for this, regardless of how whiskers and outliers are defined.

You have 21 points. If 20 of them are below 48 (or, equivalently 1 is above 48) then $$20/21 = 0.952$$ are below 48, which rounds to 95%, not 96%.

@statsstudent raises some good points about how you can go wrong with a box plot - good programs (such as SAS or R, and, I presume, others) have ways to avoid these errors, but it's easy to go wrong through naivete, ignorance or carelessness.

• I think he the OP was getting the "48" value by reading it off the boxplot graphic. If that's not the case, you are entirely correct that no boxplot would be needed. Jan 24, 2019 at 15:33

There isn't a global standard on how to draw boxplot whiskers. That being said, we cannot say that 96% of your data fall below 48 since we have no idea how many points are at that maximum point. It's entirely possible 2 or more points have the exact same value in your dataset and these points are the maximum value. In this case the top point would be plotted over by a second point (third, etc.) in your boxplot (i.e. the black diamond around $$y=55$$ in your graphic could represent $$X=x_1, x_2, x_3, x_4, x_5$$).

• The "etc" may be a little misleading, because you do know the top whisker and outlier comprise no more than $5$ points.
– whuber
Jan 24, 2019 at 16:06
• Good point @whuber. I'll fix to make this clear. Jan 24, 2019 at 17:00