Well, Mensa sucks at numbers since its very beginning. The original plan was to select 1% of the most intelligent people, but by mistake they made it 2%, and when they later found out, they decided to just keep it as it is.
“More than two sigma, that means approximately 2%, right?” “Yeah, approximately.” Later: “You meant, 2% at both ends of the curve, so 1% at each, right?” “No, I meant 2% at each.” “Oh, shit.”
If you divide a standard Gaussian at the +2 sigma boundary, the probability mass to the left will be 97.5% and to the right (“the tail”) -- 2.5%.
So two sigmas don’t mean 2.5% at each end, they mean 2.5% at one end.
On the other hand, if you use a 4-sigma interval from −2 sigmas to +2 sigmas, the probability mass inside that interval will be 95% and both tails together will make 5% or 2.5% each.
Apparently, Mensa didn’t get any better at math since then. As far as I know, they still use “2 sigma” and “top 2%” as synonyms. Well, at least those of them who know what “sigma” means.
Well, Mensa sucks at numbers since its very beginning. The original plan was to select 1% of the most intelligent people, but by mistake they made it 2%, and when they later found out, they decided to just keep it as it is.
“More than two sigma, that means approximately 2%, right?” “Yeah, approximately.” Later: “You meant, 2% at both ends of the curve, so 1% at each, right?” “No, I meant 2% at each.” “Oh, shit.”
What? 2 sigma means 2.5% at each end.
That sentence is imprecise.
If you divide a standard Gaussian at the +2 sigma boundary, the probability mass to the left will be 97.5% and to the right (“the tail”) -- 2.5%.
So two sigmas don’t mean 2.5% at each end, they mean 2.5% at one end.
On the other hand, if you use a 4-sigma interval from −2 sigmas to +2 sigmas, the probability mass inside that interval will be 95% and both tails together will make 5% or 2.5% each.
Apparently, Mensa didn’t get any better at math since then. As far as I know, they still use “2 sigma” and “top 2%” as synonyms. Well, at least those of them who know what “sigma” means.