Yeah but that doesn’t explain how the mean goes up.
In climate change the mean goes up because we are getting more extreme events, in the form of both heating and cooling events.
Lets put this in D&D terms, or at least dice rolls.
First, imagine you have two sets of dice, one blue, and one red. Blue represents cooling events, red represents heating events.
In this exercise, every individual die represents one unique event (a snowstorm, a cold blast, a heatwave, a hurricane, whatever).
Every year, you are going to roll some equal number of red and blue dice, and whatever you get as a result, those are the extreme weather events you get, and how extreme they are. Over enough years of dice rolls, the average will approach 0, but the individual years will bounce around in terms of their means, and individual events can be cover a wide range of extremes (0-6).
Climate change is like swapping some of red D6’s (six sided dice) with a few D10’s (red sided dice), and a few of your blue D6’s with D8’s. You increase range of possible extremes, tilted slightly to one side. And yes, the mean of individual years will go up (but not always), and over the course of many years, it will trend in a more positive direction.
Basically, the average doesn’t just increase monotonically or continuously. It does so through the contribution of more extreme inputs.