# 2.2 Graphing qualitative variables

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When Apple Computer introduced the iMac computer in August 1998, the company wanted to learn whether the iMac was expandingApple?s market share. Was the iMac just attracting previous Macintosh owners? Or was it purchased by newcomers to thecomputer market, and by previous Windows users who were switching over? To find out, 500 iMac customers wereinterviewed. Each customer was categorized as a previous Macintosh owners, a previous Windows owner, or a new computerpurchaser. This section examines graphical methods for displaying the results of the interviews. We'll learn somegeneral lessons about how to graph data that fall into a small number of categories. A later section will consider how to graphnumerical data in which each observation is represented by a number in some range. The key point about the qualitative datathat occupy us in the present section is that they do not come with a pre-established ordering (the way numbers areordered). For example, there is no natural sense in which the category of previous Windows users comes before or after thecategory of previous iMac users. This situation may be contrasted with quantitative data, such as a person?sweight. People of one weight are naturally ordered with respect to people of a different weight.

## Frequency tables

All of the graphical methods shown in this section are derived from frequency tables. shows a frequency table for the results of the iMac study; it showsthe frequencies of the various response categories. It also shows the relative frequencies, which are the proportion ofresponses in each category. For example, the relative frequency for "none" of $0.17=85/500$ .

Frequency table for the mac data
Previous Ownership Frequency Relative Frequency
None 85 0.17
Windows 60 0.12
Macintosh 355 0.71
Total 500 1.00

## Pie charts

The pie chart in shows the results of the iMac study. In a pie chart, each category is representedby a slice of the pie. The area of the slice is proportional to the percentage of responses in the category. This is simplythe relative frequency multiplied by 100. Although most iMac purchasers were Macintosh owners, Apple was encouraged by the12% of purchasers who were former Windows users, and by the 17% of purchasers who were buying a computer for the firsttime.

Pie charts are effective for displaying the relative frequencies of a small number of categories. They are not recommended,however, when you have a large number of categories. Pie charts can also be confusing when they are used to compare the outcomesof two different surveys or experiments. In an influential book on the use of graphs, Edward Tufte asserted
"The only worse design than a pie chart is several of them"
.

Here is another important point about pie charts. If they are based on a small number of observations, itcan be misleading to label the pie slices with percentages. For example, if just 5 people had been interviewed by AppleComputers, and 3 were former Windows users, it would be misleading to display a pie chart with the Windows slice showing60%. With so few people interviewed, such a large percentage of Windows users might easily have accord since chance can causelarge errors with small samples. In this case, it is better to alert the user of the pie chart to the actual numbersinvolved. The slices should therefore be labeled with the actual frequencies observed ( e.g. , 3) instead of with percentages.

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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Berger describes sociologists as concerned with
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