Yes, looking at the sample minimum&#x2F;maximum does change the probabilities.  You&#x27;re looking for Extreme Value Theory.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Extreme_value_theory" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Extreme_value_theory</a><p>I kept it simple (above or below average should be equal probability if your average is really average) to try and avoid that.  I have no idea what kind of distributions weather follows, and as the other guy noted weather is not fully independent either.  But it works for a simple explanation. :)<p>It&#x27;s been a long time since my stat courses and I don&#x27;t remember this stuff all that well.  Maybe there is something that expresses it better.  Either way the fact that we&#x27;re suddenly having a big run of Nth Warmest Year events is pretty suggestive that something is going on.  But you do have to look at it as a trend, particular years aren&#x27;t all that meaningful.