POLL: Math questions regarding upper elementary school (xpost to m.k.)

In article , just me wrote:
"David desJardins" wrote in message
...
Aula writes:
So what are the usual applications in real life?

Kevin posted a good example: giving the distribution of test scores to
the students in his class. It's a graphical representation of the data,
which also gives all of the raw data to the students, so if they want to
know (for example) how many students scored above them, the data is
right there.


Are there any other applications that are used at least in research or
something? While students may like to know grade distributions, that isn't
quite what I was thinking of as "real life"..... What is the real value of
knowing this type of representation of data?



Well, for some of us, preparing grade distributions IS real life.

According to Tufte, in "The Visual Display of Quantitative
Information", stem-and-leaf plots were invented by John Tukey (a
famous statistician---see
http://www-gap.dcs.st-and.ac.uk/~his...ans/Tukey.html).
This book is probably the first exposure many people (including me)
had to stem-and-leaf plots. I think that Tufte's book would be an
excellent text for middle-school or high-school students, as it
describes quite clearly how to present data well.

Tufte quotes Tukey as saying "If we are going to make a mark, it may as
well be a meaningful one. The simplest---and most useful--meaningful
mark is a digit."

Tufte gives one example of stem-and-leaf plots for the heights of 218
volcanoes. Note: Tufte dedicates one page of his 190-page book to
stem-and-leaf plots, so clearly he does not regard them as a major
topic. They are in the chapter on "multifunctioning graphical
elements," which includes a number of weird and wonderful ways of
displaying data.

My personal belief is that stem-and-leaf plots are a very minor data
presentation trick that is handy to know but not worth putting into
curricular standards. Scatter diagrams, contour diagrams, and
false-color presentation are all much more important.


--
Kevin Karplus http://www.soe.ucsc.edu/~karplus
life member (LAB, Adventure Cycling, American Youth Hostels)
Effective Cycling Instructor #218-ck (lapsed)
Professor of Computer Engineering, University of California, Santa Cruz
Undergraduate and Graduate Director, Bioinformatics
Affiliations for identification only.

In article ,
"just me" wrote:

"David desJardins" wrote in message
...
Aula writes:
So what are the usual applications in real life?

Kevin posted a good example: giving the distribution of test scores to
the students in his class. It's a graphical representation of the data,
which also gives all of the raw data to the students, so if they want to
know (for example) how many students scored above them, the data is
right there.


Are there any other applications that are used at least in research or
something? While students may like to know grade distributions, that isn't
quite what I was thinking of as "real life"..... What is the real value of
knowing this type of representation of data?

-Aula


Personally, I think it is valuable to have a lot of different tools at
your disposal to graphically represent data. You never know which ones
will make some piece of information or some connection suddenly leap out
or make more sense. You can also use it to compare two different sets
of data: say, scores from two different classes, by putting the "stem"
in the middle of 3 columns, and the "leaves" (the details from each
class) in the two side columns.

I'd never heard of leaf-and-stem (or at least didn't remember hearing
about it) until I read this thread, but it took me about 10 minutes to
find a decent explanation on a web page, and another 2 minutes to
understand it. I think it may come in handy when I'm looking at some
sorts of statistical data -- attendance figures, maybe -- but I'm not
sure yet. I also showed it to a friend who is a technical writer, and
she said she thought she could see applications for it, and was pretty
interested.

I asked both of my 17 yo's if they knew about it; one said yes and he
could explain it (he's a math sponge) and the other remembered the words
but couldn't remember what it was (she does her best to pretend school
doesn't exist at all), so obviously they ARE teaching it around here.

meh
--
Children won't care how much you know until they know how much you care

H Schinske wrote:

wrote:

It's a graphical representation of the data,
which also gives all of the raw data to the students, so if they want to
know (for example) how many students scored above them, the data is
right there.

So basically it's the same thing as a bar graph with raw data scrawled on it?
;-)

--Helen


Yes.

Jeanne

just me wrote:

"David desJardins" wrote in message
...
Aula writes:
So what are the usual applications in real life?

Kevin posted a good example: giving the distribution of test scores to
the students in his class. It's a graphical representation of the data,
which also gives all of the raw data to the students, so if they want to
know (for example) how many students scored above them, the data is
right there.


Are there any other applications that are used at least in research or
something? While students may like to know grade distributions, that isn't
quite what I was thinking of as "real life"..... What is the real value of
knowing this type of representation of data?

-Aula


There are tons of applications. This type of analysis is probably
descriptive that you use to look at the (usually categorical) data to
check for its validity. For example, in some sort of medical research,
patients may have their age, weight, temperatures recorded. Although you
can present summary stats (e.g., average, median, mode, etc.) of each
variable, the stem and leaf plot can show you a rough distribution and
from there you (the researcher) can figure out the average, median,
mode.

That said, the stem-and-leaf plot isn't used a lot in social science
research when descriptive statistics is requested.

Jeanne

"Bruce and Jeanne" wrote in message
...
There are tons of applications. This type of analysis is probably
descriptive that you use to look at the (usually categorical) data to
check for its validity. For example, in some sort of medical research,
patients may have their age, weight, temperatures recorded. Although you
can present summary stats (e.g., average, median, mode, etc.) of each
variable, the stem and leaf plot can show you a rough distribution and
from there you (the researcher) can figure out the average, median,
mode.

That said, the stem-and-leaf plot isn't used a lot in social science
research when descriptive statistics is requested.


Now that makes sense to me. I appreciate your explanation as I was having a
hard time figuring out uses. Since I work in the social sciences I might
not think as quickly of hard science applications ;-)

-Aula
--
see my creative works on ebay under aulame 123

just me wrote:

"Bruce and Jeanne" wrote in message
...
There are tons of applications. This type of analysis is probably
descriptive that you use to look at the (usually categorical) data to
check for its validity. For example, in some sort of medical research,
patients may have their age, weight, temperatures recorded. Although you
can present summary stats (e.g., average, median, mode, etc.) of each
variable, the stem and leaf plot can show you a rough distribution and
from there you (the researcher) can figure out the average, median,
mode.

That said, the stem-and-leaf plot isn't used a lot in social science
research when descriptive statistics is requested.


Now that makes sense to me. I appreciate your explanation as I was having a
hard time figuring out uses. Since I work in the social sciences I might
not think as quickly of hard science applications ;-)

-Aula


I can also see social science applications. For instance, in
transportation planning one might send out a survey asking people about
the number of cars in their household, the number of drivers, the number
of bicycles, and the primary mode of transportation. Stem-and-leaf
plots can quickly point out outliers (e.g., a household with 10 cars).

In another application (stop me, please!) can be in education policy
looking at use of PSATs: grade of student when PSAT taken, PSAT score.
Again stem-and-leaf plots would show outliers (e.g., the 5th or 6th
grader who took it).

But as a SAS programmer, I've never had a researcher ask for a
stem-and-leaf plot. They want the summary statistics.

Jeanne

On Fri, 17 Oct 2003 19:31:31 EDT, H Schinske wrote:
wrote:

It's a graphical representation of the data,
which also gives all of the raw data to the students, so if they want to
know (for example) how many students scored above them, the data is
right there.

So basically it's the same thing as a bar graph with raw data scrawled on it?
;-)

Well, as someone who works in the publishing/printing industry, my
first thought was, "Interesting... but with the right data set and
a proportional font, the plot comes out totally misleading."

I.E, if a leaf has several digits that are narrower than the
average; for example, there are lots of '1's, and other leaves have
lots of '5's, which are wider, then even if there are *more* data points in the
first leaf than the second, it will physically take up less space on the
page, and mislead the reader.

So, unless the person presenting the data is very careful about
typographic conventions, the end result would present an inaccurate
view of the data. Personally, I would just prefer a bar chart,
and have the raw data presented elsewhere. ;-)

- Rich

In article , user wrote:
Well, as someone who works in the publishing/printing industry, my
first thought was, "Interesting... but with the right data set and
a proportional font, the plot comes out totally misleading."

BEEP! You can't use stem-and-leaf plots with proportional fonts!
Mono-space fonts only!!! (Or very difficult tabular typsetting to
force each digit to have the same width.)

--
Kevin Karplus http://www.soe.ucsc.edu/~karplus
life member (LAB, Adventure Cycling, American Youth Hostels)
Effective Cycling Instructor #218-ck (lapsed)
Professor of Computer Engineering, University of California, Santa Cruz
Undergraduate and Graduate Director, Bioinformatics
Affiliations for identification only.

On Sun, 19 Oct 2003 18:51:57 EDT, Kevin Karplus wrote:
In article , user wrote:
Well, as someone who works in the publishing/printing industry, my
first thought was, "Interesting... but with the right data set and
a proportional font, the plot comes out totally misleading."

BEEP! You can't use stem-and-leaf plots with proportional fonts!
Mono-space fonts only!!! (Or very difficult tabular typsetting to
force each digit to have the same width.)

And even worse, in the context of this thread, most people write
in a more-or-less proportional fashion, so the kids could easily
end up misleading themselves with their own hand-drawn plots,
unless they are done in graph paper, to ensure that each digit
takes up the same amount of space.

(Kevin Karplus) wrote in message ...
In article , user wrote:
Well, as someone who works in the publishing/printing industry, my
first thought was, "Interesting... but with the right data set and
a proportional font, the plot comes out totally misleading."

BEEP! You can't use stem-and-leaf plots with proportional fonts!
Mono-space fonts only!!! (Or very difficult tabular typsetting to
force each digit to have the same width.)

Wow, I didn't know this and it does have an impact on the information
I'm trying to gather, so THANK YOU!

Marjorie