Opinions on how big the biggest T. rex were

[andrewsaurus rex]

It's long been my opinion that, odds are, when an adult dinosaur fossil/skeleton is found it represents and animal of average size.  For example, if future paleontologists were to randomly dig up a human male's grave, odds are that individual would have been about 5 foot 8 to 5 foot 11 tall, since that's the median height range for human males.  By chance they could dig up a man who was 5 foot 4 inches or 6 foot 6 inches, but the odds are against it.

So odds are when a T. rex is found it's of an average sized adult.  And this is pretty much born out by the fossils found to date.  Most T. rex skeletons found have averaged around 37-38 feet long, with a few (eg Sue, Scotty and Goliath) being bigger at a bit over 40 feet.

So we can know, with some confidence, that average T. rexes were about 37/38 feet and this is similar to a 5 foot 8 to 5 foot 10 male human

Human males can achieve heights of over 7 feet and even come close to 8 feet on very rare occasions.  This is about a 35% increase in dimensional size over the average male.  So can it be said, that the maximum size of a T.rex could have rarely reached 50 feet long? 

T. rex were not human or even mammals and reptiles can have even greater size ranges.  Adult crocodile males can be from 11 feet long to 20 feet.  So could T. rex have reached 55, 60 feet or more?

Maybe the Super Colossal T. rex figures aren't so out of scale afterall.

[Newt]

You're right about the statistical argument. Size distribution usually follows a "normal" or bell-shaped curve, with most individuals being near the center of the curve but a few being way out on the tails.

A complicating factor is introduced by physics: could a 50 or 60 foot Tyrannosaurus actually get around well enough to survive? When an animal's linear dimensions increase by x, its cross-sectional dimensions (including the cross-sectional areas of bones, muscles, blood vessels, etc.) increase by x², and its mass increases by x³. This causes problems, because it is gaining mass faster than it is gaining the physiological ability to support that mass.

It's possible that these animals were so close to the biomechanical limits of their body plan at typical adult size that they simply couldn't get much bigger and live. Even very tall humans have a lot of health issues imposed by their size. Statisticians call this kind of limit that causes one tail of the normal curve to end abruptly instead of petering out indefinitely is called a wall. Did Tyrannosaurus have such a wall? There's no real way to know from the limited data available, but it's worth thinking about.

[andrewsaurus rex]

yeah, i realized the rapidly increasing mass as it got dimensionally larger would be an issue.  The only encouragement i can see for that problem is the fact that sauopods attained sizes once thought impossible.....but of course they were 4 legged.

More than just bone strength i can see joints, hip, knee and ankle being the biggest problem  So, maybe Sue, Scotty and Goliath were pretty much the biggest, maybe not.  Odds would be against finding 3 such outliers in size though, so maybe they were not that uncommon, and rarer, larger individuals did exist.

Hopefully, we'll find out in time.  But certainly not finding any wouldn't mean they didn't exist.  It would just mean we didn't beat the odds and find one.

[SBell]

Digging graves is a different sample set than random chance from taphonomy.

Odds of remaining structurally identifiable and fossilizable increase with size, odds of some material being left behind by erosion will be from larger individuals, and chance of discovery increases with larger size. Couple all of that with a very limited sample size overall, so determining 'average' is a challenge.

So sampling and taphonomy biases are probably pushing our estimates closer to the above average end of the bell curve already. Couple that with histology studies, where at least Scotty was old enough for remodeling the osteology, and a reasonable hypothesis is that our largest specimens are probably closer to the largest range of normal.