'Are you above average? Why mean, mode & median matter...' blog discussion

DavidLaGuardia

thelawnet wrote: »

Just to add to that, the reality is that the 'mean' is by far the best measure to use.

Effectively you say that 4x the current return with all other things being equal Premium Bonds would be a no brainer.

I would agree that the mean is always the most important measure over a course of time, but the distribution of prizes would matter in the context of any realistic time frame and the number of draws in the sample.

If we first assume PBs produce £25 a month with £30k invested then £50 is easily the reduction in interest with carefully chosen cash accounts.

Suppose I joined a syndicate of 20,000 people that invested £50 a member with an investment that made 10%! but an eventual distribution of all of the proceeds to just one member. The mean is clearly 10% but, although I could end up with £1.1m, there is a 99.99% chance of loss for every £50 I invested. Would this really be a sensible idea every month over 10 years and what are the chances of getting anywhere the mean?

Using the mean, there would be a far greater chance of winning than in preimum bonds, but I think the chance of winning the single prize over a sample of 120 months (I've long forgotten how to work this piece of probability out) would still be too slim to stop me putting my £50 (6k into total) elsewhere despite the mean. Or am I still missing something?