# Whisker inside Box plot

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• #47502

Z
Member

Hi
I came across a box plot of data wherein the upper whisker was inside the box of the box plot.  As per my understanding, the whisker length is calculated based on interquartile range.  So the whisker has to be either of zero length or extend beyond Q3.  Can some provide an explanation?
Thanks.

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#158404

Member

How strange?! Maybe its just a bug in the software you’re using? I generally use Minitab but also Excel and sometimes Excel can be a little touchy, especially the charting functions.
I learnt yesterday that there are two types of outliers for continuous data distributions. ‘Mild’ outliers which are data points greater or less than Q3/1 +/- 1.5 x IQR. And ‘extreme’ outliers which are data points beyond Q3/1 +/- 3 x IQR.
Do a search for outliers in Wikipedia, there’s some good stuff in there. I still haven’t found a simple way of defining outliers in attribute data yet.

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#158406

Z
Member

I use Minitab 14 and this observation was on one of the graphs generated in Minitab.
That was an interesting thing on the outliers to classify them as mild and extreme.  And I agree with you on a simple way to define outliers for attribute data.
However, I would put it in terms of probabilities. In a boxplot, the probability that a point will lie beyond the whisker length is 0.3% if the data was normally distributed.  Similar logic can be extended to attribute data by saying that the probability of occurence of an event is 0.3% or more, it would be termed as an outlier.
Hope it makes sense.

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#158407

Member

Thats a neat way of looking at it Can I ask a stupid question?! How did you arrive at 0.3%? And would that apply for any sample size of attribute data?
For instance, in a sample of 10,000 would a 0.3% proportion be described as an outlier Vs a sample of only 100?

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#158409

Amandeep S Munial
Participant

Hi!
I do not know what logic Z applied.  Here’s my logic.
If the data were normally distributed, the box plot would be symmetric around the mean (= median).  Hence, Q1 and Q3 would represent cummulative probability of 25% and 75% resp. Find out the Z score to cover this much area under the curve.  Calculate total spread of box in terms of Z.  Find the Z value of the end of the whisker, assuming full length of 1.5 x IQR.  Use this Z value to find the Cumm Prob from Minitab.

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#158410

Member

I think this is what you’re referring to right? This diagram seems to explain your approach very well.
(I hope this diagram is displayed, if not I’ll post my actual results)!

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#158414

Omashi Sabachi
Participant

gREAT  eXPLANATION

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#158440

Amandeep S Munial
Participant

Hi
This is exactly what I had written.  So you got the same answers.
Good representation, I must say.

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#158890

Psyc
Participant

I have had a similar result regarding the original question, having a whisker inside the box. I would like to hear any explanations if there is one. I was using Minitab 11 at the time.
Psyc

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#159038

I’Anson
Participant

From Minitab’s Knowledgebase: