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

Entry: Beginners Guide to Mean, Mode and Median - A843248
Author: dpen2000 - U205034

I had a moment of madness and took this off peer review. Now it is back on.

If you mention problems with mean averages, you must also mention disadvanages of mode and median.

It might be useful to give some simple examples of where the mode and median may be more useful than the mean.

That well-known truth 'Most people have more than the average number of legs' is of course referring to the mean, not the mode


Azara

I liked the title change it much better desribes the article now.

Here are some examples of disadvantages with the median and mode.

The Mode is no use when you have a series of measurements that haven't been rounded such as measurements of height to 3 decimal places.
With a large sample it can be very labouris sorting them into order.

Keep at it though this is looking good.

I have standardised the sample used in examples now. Made changes to the language and taken out the problem sections out of the examples and into the Potential Problem sections. I have also replaced "SUBHEADERS" with "B" tags as the article was looking a bit too spaced out - except for in Classic Goo where it was looking fine. I have tried to be more balanced on each of the averages.

So... How is the article looking now?

dpen2000

Oh and does anyone want to be added as a researcher as I have used content almost word vertibim from this forum at times?

dpen2000

I have to say this is pretty good! In fact I can't find anything to nitpick!

I haven't got time to look into this again now. I'll come back soon.

Good Luck!

Tango

I think this is an improvement on the last version, although there still is room for improvement.

In the section on the mean, you refer mostly to a sample of numbers, but you also refer to the distribution at one point (in the example section), and in the example refer to the 'amount of numbers' rather than sample size. Also, If you are going to refer to samples, then I think you should explain the concept of a sample, that you are taking numbers from some larger population. Either that, or use group, which makes sense in any case, even if you aren't considering the numbers as part of a larger population. In either case, you should, I think, use either group, or sample (and group size, or sample size as appropriate), but not both. Also, slightly pedantically, you say that 'The next thing to do is add the numbers up'. That should be the first thing you you do, as up to that point you haven't really done anything.

Then, when you talk about the skewing of the mean, remember that it can work both ways, numbers, can be skewed towarsd the low end too, if there are a few particularly low values. The potential for this might be less however, if we are dealing with positive numbers, or at least non negative numbers, as the lowest you can go is zero. This doesn't always apply, however, and still could skew your averages if you are dealing with mostly much higher values.

Also, with the talk of outliers, the affect can be the same if there are a few outliers, rather than just one. Perhaps here, you could talk about representativity, as it is relevant here, and you mention the idea in the next. It is also related to problem 1), but with outliers the problem is in general more pronounced. Another idea might be to illustrate the point, by working out the average after including an obvious outlier, such as 100, in the group of numbers. Then the average would be 13.66666(recurring), which clear doesn't represent most of the numbers.

Perhaps similarly, there could be a brief mention of methods of avoiding this problem. You could, for example, exclude the highest and lowest so many values, to avoid outliers, although the problem is that you could end up missing a genuine trend this way.



Then, in the talk about the mode, you mention representativity. It is a bit of a mouthful, perhaps you could explain what you mean in a sentence, as it isn't that clear what you are referring to, although I assume you are talking about problem 2 of the mean.

Also, the mode is the most common number, rather than common number, and I would prefer value, rather than number here. Similarly, I think in the second sentence, the where would read better as Whereas.

In the problems of the mode, you seem to have the write idea, but I think could do with being more general. What you are describing, If I am understanding you correctly, is that the mode isn't very good with Continuous, or nearly continous data. Continuous data roughly speaking is data that can take any value in a certain range. For example, height could be considered continuous, as you could be any positive number tall, within sensible limits (usually not more than 2 metres tall). In that case, you wouldn't expect any two people to have the same height, as there are infinite possible heights, so the mode is useless.

In reality, you are limited by your measuring instruments, and what level of accuracy you want. Usually differences in height less than a centimetre can be safely disregarded. Still, even if you round of to the nearest centimentre, that leaves a number of possible values that are close, but not exactly the same, so the mode might not tell you very much, as one number might be the mode because two people have that height, rather than one, which isn't very useful information. You could round of to the nearest whole numbers, as you say. However, aa more general approach might be to turn the numbers into classes, preferably of equal widths, and consider the mode to be the class with the most values in it. It can be more useful to know that there are a large number of values in a certain interval (e.g. between 5 and 6 feet tall), than that quite a few people have a certain exact value.

The problem doesn't occur as much in discrete cases, where there are a limited number of possible values, which usually applies when you are counting things, for obvious reasons (you can't have half a person ).

The idea of classes could be discuss when talking about averages in general if you want, although that depends how far you want the entry to go.

Now finally, we are onto the median. The first sentence could be changed a bit, I think, to say something like 'This type of average is the middle number in a sample, when the numbers are put in order'. Also, I think you should mention that if there is a even group size, you take the mean of the two middle values at the start, before you go into the example. Also, I personally wouldn't reveal the median at the start, but would start by talking about how it is worked out, first. Also, you talk about an odd sample, rather than an odd sample (or group) size, which is what is appropriate here.

You then talk about a problem with the median. The hassle in working out the median may be a problem, but I think there are probably more fundamental problems here. For example, the median only reflects the value of one or two 'data points' which contrast with the mean, which includes all values. This means it is less liable to be skewed by an outlier, however. Whether this is a problem probably depends on the circumstances, but I think that it is worth contrasting the two in this way.

I think a little bit about what the different types of average are used for, and how they are use, could be useful.

For example, some stuff about standard deviation and variance and how they are used in connection to the mean etc.

Re the telephone stats - feel free to use whatever fits.

Re the "post up for PR", I meant the thread post, not the article. I'd had a little bit of vodka when I wrote it... I wasn't sure how much sense it would make.


ks

I don't think that I agree that there should be stuff on Standard deviation etc.

It's meant to be a beginners guide, and as many people get these three measures of 'average' confused then a nice simple entry that only deals with that seems appropriate.

Maybe there is a second entry which can include this and a bit more maths, but for now I think keeping it simple should be the order of the day.


ks

but surely some explanation of the uses should be included?

Although I don't think a description of the uses would be necessary, we do need a definition for outliers, which is an esoteric word that the reader can figure out from the example, but needs a solid definition in the entry.

Looks good!

What about percentile? Where does that fit in? At least the 50%-ile. Does that correpsond with one of mode/average/mean?

Awu

Let me know when we're ready to rock 'n' roll this entry into the Edited Guide.

Could someone else take charge of this article as I am very busy at the moment with exams?

Dpen2000

I'd like to see some real-world examples for mean, median and mode.

Also, I'm uncomfortable with the open bit that says there are three types of average. I was always taught that average is a synonym for mean. Median and mode can be quite different from the average (mean) of a set of values. Unfortunately, my statistics textbooks are on the shelf at work so I can't confirm that using the word average to describe the three concepts is incorrect.

Average is not a synomyn for mean, that is a common mistake, but it is just sloppy talking.

Tango

You're right... my sloppy.

Are some real-world examples in the works? I really think that would flesh out the entry.

Cheers!