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

Entry: Averages - A843248
Author: dpen2000 - U205034

I hope this is good enough for the edited guide. Please tell me if it is not.

It's certainly good enough for PR which is where this is going to be for the next seven days.

The maths people will put you in the Mastermind chair but if you stay calm and don't pass on too many, you'll be right.

Trout

Firstly, welcome to the guide. I recommend that you write a brief introduction in your personal space, so people can start conversations on your personal space.. To do that, click edit page and then write something. In particular, this lets the ACES introduce themselves. They are volunteers, whose job it is like to welcome new researcher to the guide.

Anyway, now we can talk about the entry. I think it is a good start, but it isn't ready yet for the edited guide. In particular, you need, I think, to be more precise in your language. You don't need to be excessively formal, but at times lack of precision in the entry makes it less clear. I go through the particular problems I have with the entry in order.

Firstly, in the first paragraph, you say an average 'expreses a larger group of numbers'. I would use summarises a larger group of numbers here, and I'm not sure that the word larger adds anything here, as an average is only one number, a smaller group than any other group worth calling a group (a group usually implies more than one of something.

Then in the section on the mean, you say that a distribution is 'A 'posh' satistical term for a group of numbers'. This is incorrect, a distribution is an expression of the probabilities of different values occuring. A better word here would be sample, as most of the time in statistics, the collection of numbers you are dealing with comes from a larger group of numbers. For example, if you asked ten people on the treat if they shopped at tescos, that would give a sample, from a larger group of people, that larger group most likely being the British Population, although it could be the world population, or population of the town, or whatever.

The point being that in most situation, you are talking some sort of sample, of a large population, so sample would be a better word to use than distribution. It would also allow you to use sample size, to express the number of numbers.

Also, I think the sentence 'When people think of the word average, this is the function they think about.', could be improved here, as well. I think it needs qualifying a bit, saying that 'Usually when people think of the word average....'. I also think that you could lose the word function, and have the sentence as 'Usually when people think of the word average, this is what they think about'. Also, I think the sentence here still could be improved, making it something like 'Usually when people think of the word average, this is what they mean', or probably better 'Usually when people talk about the average, this is what they mean'. There may be better ways of phrasing this too.

Then in the example, you make a point (about using close values) in the middle of explaining how you are calculating the average. I would keep the example all in one place personally.

Also, the point raised seems valid. to an extend, but is rather vaguely worded. The point I think you are making, is that you have to watch out for 'outliers', or 'dodgy' numbers, that appear not to follow the trend. For example, if you had a series of values near one, and one value of ten, the ten would be the problem point, and would most likely distort the average quite a bit. In the entry, however, you talk about needs 'close' values. This isn't strictly true, as you can deal with very spread out values, with little difficulty. The difficulty comes with values that are don't appear to be in the same range. If you get a value of a million, in a set of values mostly in the range 100 to 200, for example, you still get this distortion.

Whatever the situation, it can give you strange values for the mean, that concentrate on the 'dodgy' value, not on the other more sensible values. Those sorts of values can occur more or less 'by chance'.

There is also the linked phenemena of the mean being skewed. Sometimes you get a lot of small values, and a few really large values. Wage figures in particular are likely to do this. Here, you get a similar effect, the mean tends to be closer to the larger end, either though most values are at the lower end. You can't, however, right off the high values as mere blips, though, in this case. The opposite happen, if most values are at the high end, too.

It isn't clear which of these you mean, but both, I think are valid. In both cases, though, the issue isn't accuracy(which is what you seem to be implying) , but representativity. You can calculate the mean perfectly accurate, whatever the number is, and you can get a perfectly accurate value of the mean (within the limitations of the calculator accuracy, that is), but it may not be very useful in telling you anything about the numbers (the sample), or the population they come from. The odd 'dodgy' value may give you a mean that doesn't tell you anything useful about the numbers, whilst a skew might mean they don't reflect people in general.

Then on the mode, there are a couple of minor problems. I would avoid talking about 'popular' values. It becomes fairly meaningless when talking about such things as atomic decay, for example. (Atoms don't really have feelings ). I would substitute common (e.g. most common, and similar), if you want an arternative to most common occuring.

Also, when talking about the mode perhaps you can mention it has the opposite property to the mean, of tending to be in the region with the most values, rather than being swayed by really high or low values, as the mean can. Therefore in wage figures it is likely to be at the low end.

Then we get on to the median. This I think is the best handled of the averages in the entry. You point out quite rightly, that the median is not swayed by really large or small values. They aren't quite ignored, but they don't tend to have the same disproportionate effect that they do on the mean.

Anyway, I appologise if this appears overly harsh, and hope that I've been of help in improving your entry.


Silverfish

Not too harsh at all - judging from the half I have read so far. I am busy at the moment for the next day or two as I am away on a school trip. I will print out your comments and read them while I am away. I hope to be back here to get to work on Sunday or Monday.

Thanks for your input again. I love writing but yes, sometimes my writing is problematic. With your comments in mind I hope to improve - at least on this article.

Anyway, gotta go pack,
Thanks
dpen2000

That's all very high-falutin' Silverfish, but can you add two plus two

If there isn't already an Edited Entry about averages, there jolly well ought to be, and this has the makings of it

A word on the examples.

The most convincing argument I have come across when demonstrating the three types of average is to use the same samples set in each case.

For example, working out the average number of children per family, using the set:

1,1,2,2,2,2,3,3,6

You can find equally good justifications for using each of the methods, despite getting different results each time.

B

Sorry, my example fell down there, because I decided to change all the numbers at the last minute

It should have read: 1,2,2,2,3,3,4,6

B

I think the word range needs to be introduced here rather than sample. Perhaps also a little more about manipulation of averages according to desired results.

Hi I see this is one of your first entries to Peer Review. If you could type an introduction to your personal space then people could drop around for a chat.

I'm guessing from what you've written that you're in the process of studying GCSE Maths? I find that writing web pages on topics i'm revising helps a great deal and I expect that you do too.

Well done for using Guide ML so soon as well! most people don't try it for the first few entries.

I think it would look a little better with the addition of some and tags around the blocks of text. This would make it look less squashed together. You may also want to change to title to mean median and mode three ways of calculating averages...

Great entry, and soon to be a perfect entry! Well done.

Sample and Range are very different things, sample is the correct one for this article. Range describes the distribution of a sample, the simplist way is biggest number minus smallest number. You could mention Range, Inter-Quartile Range, Standard Distribution (no longer in GCSE Maths, so you might not know about it)

I think the proposed change is title is too long, try "Different Averages" or "Statistical Averages".

Keep up the good work, and welcome to H2G2,

Tango

I'd agree that this probably needs a title change, but then I'm not keen on either of Tango's suggestions

If you wanted to be pretentious, I'd suggest something along the lines of 'Arithmetical Calculation of Representation', although that could be seeling the Entry a little short.

B

Way's of calculating the average... I'm sure standard distribution was in GSCE Maths in 97 when i did it? it can't have changed that much since? or are they so busy trying not to use calculators that you have all the time in the real world that they don't teach so much difficult stuff any more.

They only took SD out of GCSE Maths for those taking the exam last year I think. I know I havn't had to learn it. (I'm taking my exams summer '03)

Tuts. it was one of the things only the two of us who were taking the higher paper learnt though.

To me, mode and median look pretty bizarre. But since they are really used out there (never heard of them before), it's okay that an entry deals with them.

To be well balanced, the article should also mention the weaknesses of median and mode, not only of mean. E.g., mode only makes sense if the accuracy/number-of-samples ratio is not too big, and both mode and median can't serve as ersatz for mean on large sets of numbers.

Additionally, I think it should be noted that median or mode alone are pretty useless, you have to use them together with mean. Then you can see e.g. whether your samples are standard distributed or whether there is a skew in your results.

Last but not least, give examples. Where are mode and median used? I don't know them in natural science, probably because our results are mostly according to a known distribution (mosty Gauß) and come in large numbers. But maybe financial or social sciences?

You cant say "Standard Distributed", if memory serves (as i said, i never learnt this properly), standard distribution is the mean distance of all the numbers from the mean.

I can't think of any specfic uses for mode, but it is the simplist.

Median can be used in "Box and whisker plots" along with Maximum, Mininum and Upper and Lower Quartiles (75th and 25th percentiles, median is 50th percentile). You could also add how to find median from grouped data using a cumulative frequency graph.

Tango

Did you mean normally distributed? that's the whole bell shaped curve thing. But you don't really use the mean and median to tell if a sample's normally distrubed do you? It's something to do with the percentage of all points on the distrubition being with in 1/2 or 3 standard devations from the mean.

Just realised dpen2000 might be scared off by all these comments. If he were to chagne the title to "three ways of calculating averages" or mean median and mode then it wouldn't ahve to include all the more complex statistics.

From what I've seen of him outside this conversation I don't think he will be scared off. But of course if he doesn't want to make the changes he could change the title, or he could ask one of us to do it, and put them as co-author. I think the latter is better, as it would make the guide more complete.

Well that's the ideal, but all the suggestions that have been made really would require quiet a high level on mathematical knowledge in fact far beyond what I could do.