Ware Types - Question for the group

[Tiger]

Hardly a convincing result to back your idea that averages generally
give too high numbers. In such a small material 9 to 7 can be seen as
a 50/50 result. In an increasingly larger material the numbers would
probably get closer and closer to 50/50

Not particularly adept at statistical analysis, are you?

 

[Roger Johansson]

One could argue that average gives a more fair result because it
really averages all the votes.
One could argue that median gives a more fair result because it gives
the majority more power over the minority, I think.

After thinking about this a bit more I have come to the conclusion
that average is better than median value, because the average reflects
the result with higher precision.

Let's say we have a very even vote between the values 3 and 4.
The average gives us a 3.5 value, which accurately reflects the
opinions of the group.

The median could be 3 OR 4, depending on a single persons vote, which
gives a far less accurate value, and throws the result off the average
value with a 0.5 value difference.

The midpoint method in this case would falsely give the impression
that the whole group has voted 3.0, (or 4.0).

 

[Roger Johansson]

Not particularly adept at statistical analysis, are you?

I have studied math at the university.

The difference between 9 and 7 in such a small sample does not show
any statistically valid difference between the sides.

If there was a clear tendency it should have given a lot bigger
difference.

There is no mathematical reason why there should be another result
than fifty/fifty. And the result 9 to 7 supports that.

If you throw a coin 16 times a result of 9 to 7 is perfectly normal,
but a result 15 to 1 would be very unlikely.

The more times you throw the closer you get to a fifty/fifty result.

 

[Tiger]

I have studied math at the university.

The difference between 9 and 7 in such a small sample does not
show any statistically valid difference between the sides.

You've got it exactly backwards.

If there was a clear tendency it should have given a lot bigger
difference.

Only if the sample were larger.

There is no mathematical reason why there should be another result
than fifty/fifty. And the result 9 to 7 supports that.

Actually, the result 9 to 7 *only* supports 55/45.

If you throw a coin 16 times a result of 9 to 7 is perfectly
normal, but a result 15 to 1 would be very unlikely.

non-sequitur. Has nothing to do with the question at hand.

The more times you throw the closer you get to a fifty/fifty
result.

If coins were used in voting, you'd have a good argument. Go back to
the university and demand a refund.

 

[Susan Bugher]

Not a problem, I was glad to put back a little of what I've taken out.


I'm going to have to let you know nearer the time. I have 3 on-going
projects which should be finished around the end of November (as long
as they don't suffer scope creep, which they often do), plus our local
Amateur Dramatics group has a play showing at the end of November (I
run the sound system for them). If you're still short of volunteers at
the beginning of December, let me know.

Thanks Roger, I really just wanted to say thank you again - but then I
succumbed to temptation and added the hint - didn't mean to put you on
the spot.

You are doing some interesting things - now I *really* have to resist
temptation - and not ask more about them.

Susan

 

[=?ISO-8859-1?Q?=BBQ=AB?=]

The *midpoint* is the mean - half of the people above and half
below. Bell charts to show the *distribution* would be *truly*
meaningful. Anyone?

The _mean_ is what is most commonly called the average - the sum of
the data divided by the number of data points. Vic gave means.

The _median_ is what you have called the midpoint. Also called the
50th percentile in some cases. You (Susan) gave medians.

There are two other measures of central tendency, midrange and mode.
The _midrange_ is the point midway between the highest and lowest
observed values, useless in this case. The _mode_ is the number
appearing in the data with the most frequency. More on the mode in
a bit.

It makes no sense to me to examine means in this case. The numbers
1-5 were just tags to identify the five choices available in the
straw poll. a, b, c, d, and e could just have easily been the
choices' tags, or red, orange, yellow, green, and violet.

In order for means to be useful here, we would at least have to
assume that the choices fit on a linear scale in order of 'severity'
or some such concept, and e.g. that the 'distance' between
(1)"discuss only when a warning is needed" and (2)"sometimes okay to
discuss" is exactly the same as the 'distance' between (2)"sometimes
okay to discuss" and (5)"always okay to discuss". There are other
hidden assumptions not worth going into IMO.

Using the median is also a problem, for the same reasons. The
problem with the median might not be as severe as with the mean, but
I'm not up to sussing it out right now.

However, the mode might be considered useful in the case of this
straw poll, with the technical caveat that I don't think it ought to
be considered a measure of central tendency in the usual sense. It
is the choice the plurality of voters. The significance of the
plurality's decision for each type of software is left to the reader
as an excercise.

Bell charts to show the *distribution* would be *truly*
meaningful. Anyone?

Not me, thanks. Even calling it a bell chart assumes it is a
Gaussian distribution over a linear scale. But histograms (bar
charts) would show the modes as the highest bars, and would also
show at a glance whether there were other choices close to the
mode in each case.

What follows is does not have any bearing on the straw poll analysis
itself, but I see other people making up data sets of numbers to
support the idea that means are somehow more meaningful than
medians, and I can't help pointing out that that's not such a good
idea. It's even worse than cherry-picking data sets or
cherry-picking measures to go with real data sets. At some point in
the mid-1980s the UNC Department of Sociology put the 'average'
starting salary of its recent graduates into some recruiting
material. It was well into six figures, USD. Was it accurate and
precise? Yes. Did it give the prospective student any useful
information about her future starting salary? No, at the time,
IIRC, a BS in sociology would get you something like 17-22000 USD to
start, assuming you could find employment.
ROT13:
Zvpunry Wbeqna unq erghearq gb gnxr pynffrf qhevat gur fhzzref naq
unq rnearq uvf OF va fbpvbybtl. Gur qrcnegzrag unq pnyphyngrq gur
zrna naq ercbegrq vg nf gur 'nirentr.'

 

[Susan Bugher]

I have compared Vics average numbers with your midpoint numbers:

type average midpoint (average higher than midpoint? Y or N)

Adware: 2.3 2 Y
Betaware: 3.5 4 N
CDWare: 2.5 2 Y
Commercial Software: 1.8 2 N
Crippleware: 2.2 2 Y
Demo-ware: 1.6 1 Y
Donationware: 4.3 4 N
Freeware: 5.0 5 Even
Liteware: 4.6 5 N
Malware: 1.1 1 Y
Nagware: 2.0 2 Even
Orphanware/Abandonware: 3.1 3 Y
Registerware: 3.6 4 N
Requestware: 3.8 4 N
Shareware: 1.4 1 Y
Spyware: 1.1 1 Y
Trialware: 1.8 1 Y
Warez: 0.9 1 N

9 Yes 7 No 2 Even

The result is that averages gave higher number 9 times, midpoint gave
higher numbers 7 times, and the results were identical twice.

Hardly a convincing result to back your idea that averages generally
give too high numbers. In such a small material 9 to 7 can be seen as
a 50/50 result. In an increasingly larger material the numbers would
probably get closer and closer to 50/50

What about the warez column?
0.9 to 1.0, Vics average is _lower_ than your median.

Hello Roger,

I do wish I had used a, b, c etc. instead of 1, 2, 3 etc. because IMO we
should not concern ourselves with *either* the average or the mean. We
should look at the distribution.

For some Wares there is a consensus. Everyone who has responded said
that Freeware is alway on topic (no surprise there). One person said
Warez should be on-topic, 29 (latest count) say it should be off-topic.
Some of the other wares also show a fairly strong consensus.

OTOH - CDware is one example of a very different distribution. Some
people feel it is *always* on-topic, some feel it is *always* off-topic
- and some favor the middle ground. Is there is a way to reconcile these
disparate views? IMO that is the sort of thing that needs further
discussion - and *that* requires looking at the full range of opinion
for each ware - not just an average.

The poll is flawed in various way - the meaning of the different choices
was not totally clear to some - just to give one example. Despite that I
think it could be helpful if if we discuss it in a meaningful way.

In regard to the number of participants in ACF: This web page shows
statistics for the alt.comp.freeware newsgroup. The latest available
month is August:

http://netscan.research.microsoft.c...rchfor=alt.comp.freeware&searchdate=8/31/2003

<quote>
Messages 6890
Average Message Length 25 lines
People 1093
Returnees 439
Repliers 872
1x Posters 500

Interactivity
Replies 5909
Unreplied Messages 246
</quote>

It appears to me that about 400 people *regularly* post to ACF. The
number of *regular lurkers* is of course impossible to determine.

To date 30 people have posted responses to the poll. More responses
would be most welcome.

Results to date:

Ad Beta CD Comm Cripp Demo Dona Free Lite
0 2 0 0 0 0 3 5 3
0 2 0 0 0 0 3 5 3
1 3 0 0 0 0 4 5 4
1 3 1 1 1 1 4 5 4
1 3 1 1 1 1 4 5 4
1 3 1 1 1 1 4 5 4
1 3 2 1 1 1 4 5 4
1 3 2 2 1 1 4 5 4
1 3 2 2 1 1 4 5 4
2 4 2 2 1 1 4 5 4
2 4 2 2 1 1 4 5 4
2 4 2 2 1 1 4 5 5
2 4 2 2 2 1 4 5 5
2 4 2 2 2 1 4 5 5
2 4 2 2 2 1 4 5 5
2 4 2 2 2 1 4 5 5

2 4 3 2 2 2 4 5 5
3 4 3 2 3 2 4 5 5
3 4 3 2 3 2 4 5 5
3 4 3 2 3 2 4 5 5
3 4 3 2 3 2 5 5 5
3 5 3 2 3 2 5 5 5
3 5 3 2 3 2 5 5 5
3 5 3 2 3 2 5 5 5
3 5 3 2 3 2 5 5 5
3 5 4 2 4 2 5 5 5
3 5 4 2 4 3 5 5 5
4 5 4 2 4 3 5 5 5
4 5 5 2 4 3 5 5 5
5 5 5 3 5 4 5 5 5

-----------

Mal Nag Orph Reg Requ Shar Spy Trial Warez:
0 0 0 1 1 0 0 0 0
0 0 0 2 3 0 0 0 0
0 0 1 2 3 0 0 0 0
1 1 1 2 3 1 1 1 0
1 1 1 3 3 1 1 1 0
1 1 2 3 3 1 1 1 0
1 1 2 3 3 1 1 1 0
1 1 2 3 3 1 1 1 1
1 1 3 3 3 1 1 1 1
1 1 3 3 3 1 1 1 1
1 1 3 3 4 1 1 1 1
1 1 3 3 4 1 1 1 1
1 2 3 4 4 1 1 1 1
1 2 3 4 4 1 1 1 1
1 2 3 4 4 1 1 1 1
1 2 3 4 4 1 1 1 1

1 2 3 4 4 2 1 2 1
1 2 3 4 4 2 1 2 1
1 2 3 4 4 2 1 2 1
1 2 4 4 4 2 1 2 1
1 3 4 4 4 2 1 2 1
1 3 4 4 5 2 1 2 1
1 3 4 4 5 2 1 2 1
1 3 4 4 5 2 1 3 1
1 3 4 5 5 2 1 3 1
1 3 5 5 5 2 1 3 1
1 3 5 5 5 2 1 3 1
3 4 5 5 5 2 2 3 1
4 4 5 5 -- 2 3 4 1
-- 5 5 5 -- 3 3 5 5


------------

Responders:

Alastair Smeaton <[email protected]>
Bjorn Simonsen <[email protected]>
Blinky the Shark <[email protected]>
Boomer <[email protected]>
DAN <[email protected]>
Darrien <""Darrien_Lambert\"@[email protected]>
Dewey Edwards <[email protected]>
Harvey Van Sickle <[email protected]>
Jim Scott <[email protected]>
John Corliss <[email protected]#>
Klaatu <[email protected]>
OhnO the Clown <[email protected]>
Omar© <[email protected]>
Onno <[email protected]>
(e-mail address removed)
Roger Johansson <[email protected]>
Spooka <[email protected]>
Steve H <[email protected]>
Susan Bugher <[email protected]>
Tech Zero <[email protected]>
Vegard Krog Petersen <[email protected]>
bambam <[email protected]>
burnr <[email protected]>
digitalMOSQUITO <[email protected]>
dkg_ctc <[email protected]>
dszady <[email protected]>
(e-mail address removed)
stan <[email protected]>
(e-mail address removed)
vsj <[email protected]>

--------

1. off-topic - discuss only when a warning is needed
2. off-topic - brief mention sometimes okay (for comparison etc.)
3. ???-topic - sometimes okay to discuss
4. on-topic - usually okay to discuss
5. on-topic - always okay to discuss

Following is a list of the ware types shown in the Pricelessware
Glossary. If you need to refresh your memory of a ware definition see:

http://www.pricelessware.org/2003/info2003PL.htm#Wares

-----------

Adware:
Betaware:
CDWare:
Commercial Software:
Crippleware:
Demo-ware:
Donationware:
Freeware:
Liteware:
Malware:
Nagware:
Orphanware/Abandonware:
Registerware:
Requestware:
Shareware:
Spyware:
Trialware:
Warez:

 

[Susan Bugher]

It makes no sense to me to examine means in this case. The numbers
1-5 were just tags to identify the five choices available in the
straw poll. a, b, c, d, and e could just have easily been the
choices' tags, or red, orange, yellow, green, and violet.

Amen to that - if I'd seen your post before I sent mine I would have
borrowed that paragraph.

Susan

 

[Roger Johansson]

Amen to that - if I'd seen your post before I sent mine I would have
borrowed that paragraph.

That would not solve the problem of reporting the vote in an accurate
and compact way.

Let's say yellow stands for what we have called 3, and green for 4.

If half of the voters have voted yellow and the other half green, the
midpoint is yellow or green, should the result be reported as yellow,
green, or yellowgreen? yellow-green 51/49 ?

The average value 3.5 gives an accurate reflection of the votes in
such a case. Such a notation takes very little space compared to other
alternatives.

A midpoint value like 3, or 4, would misrepresent the vote grossly.

 

[REMbranded]

It's your *assumptions* that needs checking. Averages give numbers that
are too high - as I suspect you know.

The *midpoint* is the mean - half of the people above and half below.
Bell charts to show the *distribution* would be *truly* meaningful.
Anyone?

I'm not sure about that Susan. Since we answered numerically as to how
the ware fits in here a simple average does give the answer as to the
1-5 ranking of those who responded.

I hope more people will respond to the poll. For now - here again are
the results to date - with the mid-point denoted by a blank line above
and below for ease of reference. Look at the numbers in the Warez column
to see why I thing averages are a bad idea.

Intersting poll. I know Vic mistakenly rated warez as a 5. That's the
only overt mistake that I caught. I am curious as to why the
abandon\orphanware scored so low. Is Proxomitron really a 3.1?

Maybe it was a misunderstood category, I dunno. I rate it as a 5, but
I might be wrong, or outgunnned.

 

[Vic Dura]

Intersting poll. I know Vic mistakenly rated warez as a 5. That's the
only overt mistake that I caught. I am curious as to why the
abandon\orphanware scored so low. Is Proxomitron really a 3.1?

Maybe it was a misunderstood category, I dunno. I rate it as a 5, but
I might be wrong, or outgunnned.

The warez averaged out to 0.9

 

[Klein]

If you think it is helpful to suggest a

commercial alternative here, then of course, you're free to do so. If
no one objects, the next time someone does it and someone objects, they
will cry, "foul," and they will be justified. It opens the door for
anyone to suggest any commercial product.

My personal view of freeware is that it is always considered in comparison
to the equivalent commercial product. I still buy software occasionally
because the value/price is so much better than the freeware alternative. To
say something like, "I tried XXX and YYY freeware products, but ended up
buying ZZZ because it worked so much better." is just part of the freeware
equation. I just hate to see someone wade through a freeware quagmire
(which I have already done) for something that is important to them when a
$30 product will make it a breeze. To me, the mention of the $30 product is
very important in the analysis.

Comparision with, and analysis of, commercial software alternatives is very
much on topic. It is misdirected moderation that is far too often off
topic.

 

[Tiger]

Comparision with, and analysis of, commercial software
alternatives is very much on topic. It is misdirected moderation
that is far too often off topic.

What about "alt.comp.freeware" do you not understand? Notice, it
doesn't say "alt.comp.software." You're either trolling or you're
incredibly dense. Either way, I'll not be seeing your response. Bye.

 

[Tiger]

That would not solve the problem of reporting the vote in an
accurate and compact way.

Let's say yellow stands for what we have called 3, and green for
4.

If half of the voters have voted yellow and the other half green,
the midpoint is yellow or green, should the result be reported as
yellow, green, or yellowgreen? yellow-green 51/49 ?

The average value 3.5 gives an accurate reflection of the votes in
such a case. Such a notation takes very little space compared to
other alternatives.

A midpoint value like 3, or 4, would misrepresent the vote
grossly.

Like I said, go back to the university and get a refund. You're making
an ass of yourself. Oh and btw, bye.

 

[=?ISO-8859-1?Q?=BBQ=AB?=]

That would not solve the problem of reporting the vote in an
accurate and compact way.

You are right. It only points out that attempting to use averages
of the tags does not help in reporting the vote in an accurate and
concise way or in any way at all. Means and medians are the wrong
tools for the job.

Let's say yellow stands for what we have called 3, and green for
4.

If half of the voters have voted yellow and the other half green

Let's not. Fabricating a data set (also mentioned in my earlier
post) illustrates nothing here.

 

[Aaron]

< snip >

A much more bizarre interpretation is where people want a newsreader
and you suggest one that only natively does online nerwsreading. Kind
of like suggesting a car with only two wheels. Despite your obvious
"denial mode" many people in the world want/use offline newsreaders.

Your fanatical enthusiasm about XNews does not help such people.

Settle down boys, you can settle your long standing feud about Xnews
elsewhere. This thread's hot enough as it is.

Regards, John.

Aaron (my email is not munged!)

 

[Susan Bugher]

Intersting poll. I know Vic mistakenly rated warez as a 5. That's the
only overt mistake that I caught. I am curious as to why the
abandon\orphanware scored so low. Is Proxomitron really a 3.1?

Maybe it was a misunderstood category, I dunno. I rate it as a 5, but
I might be wrong, or outgunnned.

http://www.pricelessware.org/2003/info2003PL.htm#Wares

<quote>
Orphanware/Abandonware: software that the original author or company no
longer offers to the public (used when author cannot be located or
company is no longer in existence). May not be freeware. May not be
legal to obtain and use it.
</quote>

IMO the sometimes/usually/always on-topic *votes* may be more a
difference in *style (for lack of a better word)* than a difference in
substance.

IMO a response with 5 for Orphanware/Abandonware *combined* with a 1 for
Warez means: if the Warez is excluded *first* the *remaining* programs
are always on-topic. FWIW: I gave Orphanware/Abandonware a 3 because it
includes some Warez. I gave Warez a 1. Sounds to me like we are in
agreement but our *votes* are not.

Susan

 

[Aaron]

Sorry for the top post.

For what's it's worth here are the scores I calculated based on 29 entries.
There are some scores (2 each for
CDware,commerical,cripple.mal,nag,trial,spy,warez and demo and 1 for
Adware, Orph, ) which are given as zero, which is strange, given that you
are supposed to pick 1-5 . I took it at face value zero.

If I excluded those values,

The median for

Demoware would be 2 (instead of 1)
Cdware would be 3 (instead of 2)
Trialware would be 2 (instead of 1)
Shareware would be 2 (instead of 1).

The means would be higher for all of course as well. But I think taking
zero is okay, I'm guessing, some (many?) voters treated their votes onn
interval scale rather then ordinal scale as requested.

Then there are entries with dashes, I'm not so sure how to treat them, did
the voter abstain? Those I removed from the dataset, the scores below
exclude these entries.


Means are rounded to 1 decimal place.
Std deviations are rounded to 1 decimal place (assuming they are relevant
!).

Any fool can calculate the scores, it's the interpretion part that requires
a genius or a spindoctor!

Adware
======
Median= 2.0
Mean = 2.3
Mode = 3
Inter-Quartile range= 2
Standard deviation= 1.1


Betaware
========
Median= 4.0
Mean = 3.9
Mode = 4
Inter-Quartile range= 2
Standard deviation= 0.9


CDware
======
Median = 2.0
Mean =2.5
Mode= 2
Inter-Quartile range= 1
Standard deviation = 1.2


Commerical
==========
Median =2.0
Mean= 1.8
Mode = 2
Interquartile range= 0
Standard deviation = 0.6


Crippleware
===========
Median = 2.0
Mean = 2.2
Mode = 1
Interqualie range = 2
Standard deviation = 1.3


Demo
====
Median = 1.0
Mean = 1.6
Mode = 1
Interquartile range = 1
Standard deviation = 0.9


Donationware
============
Median = 4.0
Mean = 4.3
Mode = 4
Interquartile range = 1
Standard deviation = 0.6


Freeware
========
Median = 5.0
Mean = 5.0
Mode = 5
Interquartile range = 0
Standard deviation = 0.00

Liteware
========
Median = 5.0
Mean = 4.6
Mode = 5
Interquartile range = 1
Standard deviation = 0.6



Malware
=======
Median = 1.0
Mean = 0.9
Mode = 1
Interquartile range = 0
Standard deviation = 0.7

Nagware
=======
Median = 2.0
Mean = 1.8
Mode = 1
Interquartile range = 2
Standard deviation = 1.2

Orphanware/Abandonware:
======================
Median = 3.0
Mean = 2.7
Mode = 3
Interquartile range = 1
Standard deviation = 1.3


Registerware:
============
Median = 4.0
Mean = 3.0
Mode = 4.0
Interquartile range = 1
Standard deviation = 1.0


Requestware:
===========
Median = 4.0
Mean = 3.0
Mode = 4.0
Interquartile range = 1.5
Standard deviation = 1.0

Shareware
=========
Median = 1.0
Mean = 1.2
Mode = 1&2
Interquartile range = 1
Standard deviation = 0.7

Spyware
=======
Median = 1.0
Mean = 0.9
Mode = 1
Interquartile range = 0
Standard deviation = 0.6


Trialware
=========
Median = 1.0
Mean = 1.6
Mode = 1
Interquartile range = 1
Standard deviation = 1.2

Warez
=====
Median = 1.0
Mean = 0.9
Mode = 1
Interquartile range = 0
Standard deviation = 0.9

There you go... Not that it will settle anything....

The _mean_ is what is most commonly called the average - the sum of
the data divided by the number of data points. Vic gave means.

The _median_ is what you have called the midpoint. Also called the
50th percentile in some cases. You (Susan) gave medians.

There are two other measures of central tendency, midrange and mode.
The _midrange_ is the point midway between the highest and lowest
observed values, useless in this case. The _mode_ is the number
appearing in the data with the most frequency. More on the mode in
a bit.

From what I can see the mode alone is pretty useless. For most categories,
the votes tends to be around 2 values. Manually counting, I noticed a lot
of cases, but for 1 vote or 2 there would be a co-modal value.

It makes no sense to me to examine means in this case. The numbers
1-5 were just tags to identify the five choices available in the
straw poll. a, b, c, d, and e could just have easily been the
choices' tags, or red, orange, yellow, green, and violet.

I disagree with your example.It could be argued that while we are talking
about catergorial data , the poll is on an ordinal scale (eg from most
favourite to least favourite, from less ontopic to most on topic) and not
on a nominal scale (red,green,yellow etc)

The difference is that you can order the choices and count them, but you
can't measure. For nominal data, you can't even order them.

In order for means to be useful here, we would at least have to
assume that the choices fit on a linear scale in order of 'severity'
or some such concept, and e.g. that the 'distance' between
(1)"discuss only when a warning is needed" and (2)"sometimes okay to
discuss" is exactly the same as the 'distance' between (2)"sometimes
okay to discuss" and (5)"always okay to discuss". There are other
hidden assumptions not worth going into IMO.

That would be on an interval scale. That would mean as you pointed out
choosing a (2) means X times stronger then choosing a (1) and (3) is X
times stronger then (2). You have to somehow operationalise the words
"usually", "sometimes".

Not me, thanks. Even calling it a bell chart assumes it is a
Gaussian distribution over a linear scale. But histograms (bar
charts) would show the modes as the highest bars, and would also
show at a glance whether there were other choices close to the
mode in each case.

For what's it worth when manually counting modes, in most cases there is
another choice that has 1 or 2 less votes then the mode. This probably
relates to the fact that in the voting scale, the difference between say

1. off-topic - discuss only when a warning is needed
2. off-topic - brief mention sometimes okay (for comparison etc.)

Is too vague, and it's probably a coin toss.

What follows is does not have any bearing on the straw poll analysis
itself, but I see other people making up data sets of numbers to
support the idea that means are somehow more meaningful than
medians, and I can't help pointing out that that's not such a good
idea.

Of course the problems of mean versus median when dealing with extreme
values is well known, but in this case it doesn't really make a big
difference. Both measures have their place, if you know what you are doing.
In our case, it doesn't really make a difference.



Aaron (my email is not munged!)

 

[Andy Mabbett]

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


Don't really know what this is.

HTH.

 

[Andy Mabbett]

I agree however that it would be nice to see someone calculate the
median and standard deviation. I am to lazy to do so myself :-(
although I'm not certain about their statistal validity with this kind
of data.

Data collected from a self- selecting subset of a population, such as
this, has virtually no statistical validity.