Good day all, I hope everyone is great!. It is hot, near 35 in Toronto, smog alert today. I wanted to share a bit as I toggle unit 1:

This issue of 'random selection' is so fascinating as to the power it has in evening out, or smoothening or dampening any outrageous scores. Having 'equal' chance to be selected and included is likely the most powerful tool in statisitcs, as to being able to generalize results to a parent population.

Also, as a refresher to me, as I had to go back to this issue and it remains so fascinating what the behaviour of numbers can be: the central limit theorem states that in large enough samples, the distribution of a sample mean approximates a normal curve, amazingly, regardless of the shape of the distribution from which it is sampled. The larger the value of the sample size (n) the better the approximation to the normal. I include a good visual example web site of what occurs in the sample distribution as I read this today:

http://www.statisticalengineering.com/central_limit_theorem.htm

I am hoping to spurn some debate on the issue of this '30' as a rule of thumb for it is both fascinating and confusing still at times, that is, when the size approaches or exceeds 30.