h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Tango, what you mean is probably 'standard degression'.

And, yes, I meant normal distribution. For normal distribution, mean = median = mode. If there is a significant difference, it's 'skewed', ie not normally distributed. However, there are also other distributions for which all three values are equal.

I didn't propose to include this high level math stuff. But the entry suggests that mean has problems that median and mode solve. After all, the arithmetical mean value is the only truely legitimated 'average'. The two others are helpers that help you to classify the distribution. I think heuristical methods (eg excluding rogue values from the mean calculation) are better than using mode or median.

Besides that the mean value is in fact *easier* to calculate. You don't have to sort the values which can be a very costly undertaking. If you have values like 3.134265, 5.46532, 4.843726, ... then mode can't be calculated at all (unless you have very very many values). If you have already calculated the mean average, and one new value should be added, you can easily do so; for median and mode average however, you have to look at all older values again.

And added to all this if you are explaining your results to others then the mean is the most commonly understood.

I've always heard it called standard distribution, not standard digression. They sound like they mean the same thing though.

This is a good first entry.
I don't think it needs to talk about standard deviation and so on - save that for another entry. The standard deviation isn't really an average in the same sense as mean, mode, and median.

On the other hand, it'd be interesting to show the link with politics: the government tend to talk about average wages and use the mean, the opposition tend to use the median. This is because there are a few people with fantastic riches, and this makes the mean significantly higher than the median. This is just one of the many ways of distorting statistics to show what you want to show.

It'd also be useful to talk about weighted averages. An example of this is Labour's pledge to get spending (as a % of GDP) in the UK up to the European average. Labour calculated this average by taking the percentage in each country and taking the average. But this gives as much weight to Luxembourg as Germany, which is nonsense. A better calculation would weight the figures so that the figures are counted in proportion to the size of the country.

-Martin

Well well well... yes, most of what you are saying does not make a lot of sense. I am learning today how to do such things as 25 and 75 percentile quartet as well as get a medium from a curve but really I am not confident enough to do a lot more than averages.

I would have no problem with having contributions to the article from other researchers here. As I see it, h2g2 is a community and if I can't learn to be community spirited, I might as well leave. But as it is, I am fine with Tango doing some stuff with my article.

The question I need to decide with Tango or whoever is: When do they want to take over control of the article or do I add in there bits as they post them in here? i.e. how will this work out practically. I think I want to make a few more adjustments to the article like make the examples use the same numbers.

Anyway, I'll see what others think.

dpen2000

The other option is of course to just do the three averages in this article. I would prefer this option as it would mean a shorter article for people to read through. I am myself thinking about doing another article on frequency tables, classes and how the averages work with these classes because I learnt that today and would be confident enough to make a start. The problem with an article on frequency tables is that it would require tables to be included and I am not sure if this is allowed.

Anyway, please do talk to me about these things,
dpen2000

> "The other option is of course to just do the three averages in this article."

I think that'd be reasonable. You could title it 'Simple Statistical Averages' if you like, so people didn't expect to see treatises on more advanced stuff.

-Martin

What about a title of "Mean, Median and Mode - A summary", then you could link to another, more comprehensive, entry that I am willing to write (with help, as I am only 15, so some of my higher level maths is very patchy). What do u think?

Tango

As far as I have heard here, while there are other averaging methods such as standard deviation etc, there is not miles more that I need to write on these three averages so I would say there is no need to call it a summary. I have just put in an application to do a project under the initial title of Statistical Analysis of Numbers of which my averages article would be part of. The application is at http://www.bbc.co.uk/dna/h2g2/brunel/F42014?thread=215164 dpen2000

Whoa! Slow down there! You want to do an entire uni project on Statistics? No offence, but if you are only doing GCSE level stats then I don't think you really know enough about statistics to do a uni project on it. I know I don't, and you seem to be at about the same level as me. Why don't you stick with this page, and see where it all goes from here.

I see what you mean about this not really being a summary. This is certainly not all that can be said about mean median and mode, though. There are people who spend years doing statistics degrees, who could probably have a lot more to say on the subject. What about "Mean, Median and Mode for Beginners"?

BTW SD is not an average, it is a type of range. Range and average are very different things that are often used in conjunction to describe a sample. 25th and 75th percentiles (lower and upper quartiles) are used to find the "inter-quartile range" (UQ-LQ), this eliminates and extreme values from the range. (that is off topic, but i thought i'd explain it anyway because I am v bored)

Tango

Okay.. you're right. I've just withdrawn my project from the university admisions board. The unfortunate problem is I just withdrew from peer review. I think I must be mad.

dpen2000

You can resubmit to PR, that's not a problem. We will have to start on a new thread though, but i think we can cope.

Wow there's some technical stuff in these replies! Far too much for me in my current state, but having just registered I thought I'd try to do something usefull...


Might I (humbly) suggest including some real-world examples?

From telephony there are some interesting statistics that people can use to understand the difference more easily...

* The mean telephone call is normally around two minutes thirty seconds.
* The modal telephone call is normally less than five seconds.
* The median telephone call is normally around forty seconds (about two seconds is usual).

The interesting thing is why get these numbers?

Calls split into about three different types:
* Very short - a failed call. You phoned and got somebody's voicemail and don't leave a message; a fax failed (you put in the person's voice number by mistake).
* Fax - a single page takes about 40 seconds.
* Conversation - well... People can talk for quite some while.

With failed faxes and conversations being just a few seconds long this causes a modal around two seconds, maybe three.

With single page faxes being between 35 and 50 seconds this causes such a huge block of calls (but still smaller than the connected, but failed calls) that nearly always falls in the middle of an ordered list of call lengths.

Because some people (... I wasn't going to say who, really, but my SO has to be up there somewhere) can talk for a very long time it skews the mean much higher. Because that the calls are long, but infrequent they don't alter the median or modal at all.

A graph of number of calls against time shows a huge peak between one and ten seconds and a slightly smaller peak between 35 and 50 seconds. After that it tails off.


Anyway, I'm pleased that this post isn't up for PR.

Good luck with the entry

<> eh... i'm confused ... why? Anyway it is up for PR. It is at http://www.bbc.co.uk/dna/F48874?thread=215197 Also, thanks, Kay Ess, for that stuff on telephone statistics. Is it okay if I just copy it straight into the article with little change to it and name you as a researcher? Oh, yeah, could you reply in the new PR thread? Also just like to inform those that are following this thread that my latest updates are in the other thread and I would be interested in responses. dpen2000

It is a good entry, however....

It could be formatted with a bit more white-space, to stop the reader from being scared away - It took me two attempts to read it - the first time, I saw all those number thingys and was scared off.

But don't listen to me - my 'A' level maths result wasn't the best in the world (sob)

BaffledGreg

Urgh... the memories...

I might be a bit late with this, having been paying attention!

As a maths student (currently studying OU Stats degree) I feel that it would be really useful to have a very brief summary at the end.

This is because most people I know who do Maths degrees, do them because they don't have to read lots or write lots.

It is a good entry though, and a very useful and clear explanation of something that for some reason seems to confuse lots of people, even at degree level.

Hey Kay Ess,

I've used your telephony example in the final, subbed version of the Averages entry (now 'A Beginner's Guide to Mean, Median and Mode' at A956289), and because I thought it is such a fine example I've also given you credit. Hope you don't mind.

SchrEck Inc.