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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

Is there any normative that regulates the use of silver nanoparticles?
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what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
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what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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it is a goid question and i want to know the answer as well
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
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s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
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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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