Hi all,

Quick question...

I know to work out the average (or mean) of a list of numbers you add them up and then divide the total by the number of numbers.

BUT!

Can you do it this way...

Take the first number.
Add the second number and divide the total by 2.
Add the third number and divide the total by 2.
...
Add the nth number and divide the total by 2.

Does that work?

Thanks!

no

Are you sure?

Hmm...

It seems that it doesn't work but my brain doesn't accept that fact.

LOL!

There are three types of average. Mean, mode and median.
One is the total divided by the number of samples, one is the most common number in the samples and one is the middle number if put in order. I forget which is which.

Ah, I've just figures out why it doesn't work.



LOL!

Brain fade moment for a second there

I can prove it doesn't work by means of a trivial counterexample, but it's bugging me. And I guess it makes sense, although initially I half expected it to work.

Trivial counterexample:


And I guess it makes sense. If you have an average, then you're averaging your cumulative average with each new piece of data, so you increase the weighting of the nth datum as n increases exponentially, ie:

Bugger, sorry it took so long! I was scribbling on a copy of the metro in green highlighter (not that green is a particularly slow colour, mind) and then used a quick online LaTeX compiler.

LOL, no problem.

I had the same feeling as you and then the same thought (i.e. the weighting of the accumulative average.

Sorry, but that post contains sooooo much win.

We really need rep on here.

Hmmm, I think I'd be into negative rep overall! What's so win-y about that post?

Post counts and sticky threads are the devils work.

Rep should replace post count IMO.

The Metro, the green highlighter, the comment about the green highlighter, the "quick" LaTex compiler, the rushed nature of it, etc...

It is a very funny and perfectly put together post

Almost worthy of Douglas Adams

Why thank thee. And I was still too slow!

I now know you know now, but it amused me that you thought of it. I remember following the same logic many years ago, although I forget what the project was.

The simplest way is to keep a tally of how many samples are taken, and a rolling total of all previous samples. At the very least, you need to know how many samples there have been so you can adjust the weighting accordingly.

Producing a "rolling average" is a bit of a pain in practice, because you require infinite precision numbers. Otherwise, you eventually reach a saturation point where no further changes to the readout are possible.

I'd be interested in what algorithms are used to display the "average fuel consumption" on trip computers. I know they're not all the same, and I suspect many of them weight recent samples more heavily. That is to say, it's a different kind of "average" all together.