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This section gives step by step directions on how to convert a quick box plot to a box plot with outliers.

Now that you know how to find a quick box plot, one made up of the minimum value, first quartile, median, third quartile and maximum value we are going to go a step further and do the mathematics for an outlier box plot. So instead of looking at the data and saying well that value looks different or far away from the rest of data so it must be an outlier we will have a concrete way of determining if data values are outliers.

An outlier is a data value that is well separated from most of the other data in a distribution. Judging whether or not a value fits this definition relies on qualitative judgment. What is needed is a more precise rule for identifying outliers. Such a rule has been described by a statistician named John W. Tukey.

Finding outliers

Tukey uses the following procedure for identifying outliers.

  1. Define the location of a FENCE as the value that is 1.5 times the interquartile range below the lower quartile, or above the upper quartile.
  2. Define the UPPER FENCE as the upper quartile plus one step. UPPER FENCE = Q3 + 1.5 (IQR)
  3. Define the LOWER FENCE as the lower quartile minus one step. LOWER FENCE = Q1 - 1.5 (IQR)
  4. Any value that is less than the Lower Fence or that is greater than the Upper Fence is declared an OUTLIER

The outlier box plot

In order to draw an outlier box plot, you need to find two additional values, sometimes called the ADJACENT values. The Lower Adjacent value is the actual value in the distribution that is closest to the Lower Fence, but which is not less than the Lower Fence. Similarly, the Upper Adjacent Value is the actual value in the distribution that comes closest to the Upper Fence, but that is not greater than the Upper Fence.

Let’s go through an example to understand the process of constructing an outlier box plot. This example uses data on the number of hysterectomies performed by male doctors.

The data for the male doctors are given as follows:

20 25 25 27 28 31 33 34 36 37 44 50 59 85 86

The first step is to determine the five number summary (a short hand for listing out some of your statistics). The five number summary starts with the sample size (minimum, first quartile, median, third quartile, maximum value). For this data the five number summary is 15(20, 27, 34, 50, 86).

A quick box plot based on this five number summary would look like the graph below:

From the five number summary we can determine that the Interquartile Range is

IQR = Q3 - Q1 = 50 - 27 = 23

Now that we have the IQR, we can calculate the location of the Fences.

LOWER FENCE = Q1 – 1.5(IQR) = 27 – 1.5(23) = 27 - 34.5 = -7.5

UPPER FENCE = Q3 + 1.5(IQR) = 50 + 1.5(23) = 50 + 34.5 = 84.5

You will notice that the Lower Fence represents an impossible value for number of hysterectomies, -7.5. Don't be concerned about this. The fences are just boundaries that let us determine if there are any outliers. In this situation, we know there are no outliers at the low end of the distribution since a doctor cannot perform less than 0 surgeries. Also, the lowest value is 20, which is not lower than -7.5, so, once again, there are no outliers at the low end of the distribution. In fact, we have just found the LOWER ADJACENT VALUE. Because 20 is the lowest value that comes closest to the Lower Fence without being less than the Lower Fence, the Lower Adjacent Value is 20.

To find the Upper Adjacent Value, look for the value that comes closest to 84.5 without being greater than 84.5. The Upper Adjacent Value is therefore 59. Any value that is greater than the Upper Adjacent Value is considered an outlier. In this case there are two outliers at the upper end of the distribution, 85 and 86. The outlier box plot for this data set would look like the graph shown below:

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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