# 2.5 Stem and leaf displays

Introduction to stem and leaf plots.

A stem and leaf display is a graphical method of displaying data. It is particularly useful when your data arenot too numerous. In this section, we will explain how to construct and interpret this kind of graph.

As usual, an example will get us started. Consider . It shows the number of touchdown (TD) passes

Touchdown Pass: In American football, a touchdown pass occurs when a completed passresults in a touchdown. The pass may be to a player in the end zone or to a player who subsequently runs into the end zone. Atouchdown is worth 6 points and allows for a chance at one (and by some rules two) additional point(s).
thrown by each of the 31 teams in the National Football League in the 2000season.

A stem and leaf display of the data is shown in the below. The left portion of the table contains the stems. They are the numbers3, 2, 1, and 0, arranged as a column to the left of the bars. Think of these numbers as 10's digits. A stem of 3 (forexample) can be used to represent the 10's digit in any of the numbers from 30 to 39. The numbers to the right of the bar areleaves, and they represent the 1's digits. Every leaf in the graph therefore stands for the result of adding the leaf to 10times its stem.

 3|2337 2|001112223889 1|2244456888899 0|69

To make this clear, let us examine this more closely. In the top row, the four leaves to the right of stem 3 are 2, 3, 3, and 7. Combinedwith the stem, these leaves represent the numbers 32, 33, 33, and 37, which are the numbers of TD passes for the first fourteams in the table. The next row has a stem of 2 and 12 leaves. Together, they represent 12 data points, namely, two occurrencesof 20 TD passes, three occurrences of 21 TD passes, three occurrences of 22 TD passes, one occurrence of 23 TD passes, twooccurrences of 28 TD passes, and one occurrence of 29 TD passes. We leave it to you to figure out what the third row represents.The fourth row has a stem of 0 and two leaves. It stands for the last two entries, namely 9 TD passes and 6 TD passes. (Thelatter two numbers may be thought of as 09 and 06.).

One purpose of a stem and leaf display is to clarify the shape of the distribution. You can see many facts about TD passesmore easily in than in the . For example, by looking at the stems and the shape of the plot, youcan tell that most of the teams had between 10 and 29 passing TDs, with a few having more and a few having less. The precisenumbers of TD passes can be determined by examining the leaves.

We can make our figure even more revealing by splitting each stem into two parts. The below shows how to do this. The top row is reserved for numbers from 35 to 39 and holds only the 37TD passes made by the first team in the . The second row is reserved for the numbers from 30 to 34 and holds the 32, 33, and 33 TD passesmade by the next three teams in the table. You can see for yourself what the other rows represent.

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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