Well, If at any given simultaneous point in time, temperature readings were recorded for many points at various longitudes and latitudes distributed at regularly spaced intervals, the readings could be summed and then divided by the number of readings. That resultant value would be an approximate average temperature for the whole earth for the specific instant.
In the USA, we have NOAA temperature data stretching back a very long time. That data has high and low values for specific dates at specific stations. Those values can be used to derive an average value for the date. Surprisingly, the average calculated thusly is quite consistent over time. my studies revealed that by calculating an average for say January 5 over a 50 year period and comparing that value with the calculated value for the current year there can be variance. I learned that for the years in question, the average temp for a specific January date was slightly in excess of the historic average.
I actually did all that back in the late 80’s. The result was that for four or five years in a row, the current average value marginally exceeded the historic value.
What that meant to me was that there was no variation in the color patterns of 100+ Wooly Worms correlating to the “warm” weather that year. And, the data thus applied did not show that there was wooly worm color variation in October adequate to predict a warm or cold winter
But I think the point the author is trying to make is that such an average may not provide much insight into what is really happening. It also may not even reflect reality in a situation where the data is very noisy, and the system you are interested in may not be well represented by the chosen sample locations.
As one example of the challenges involved, if you had a network of 100 temperature sensors, the average over 1 year could move up by one degree if the average temperature at each of the sensors increased by one degree during every day of the year, or if the temperature increased at ten of the sensors by 10 degrees during every day of the year, or if the temperature increased by 10 degrees at ten of the sensors randomly, with a given sensor changing by 10 degrees for about a month per year.
In each case the effects of the temperature changes would be different. But the average is the same.
Given the wide variance in temperatures measured locally, and during the course of each day, small shifts in the average may or may not represent significant changes.
The people arguing that climate change is a pressing danger need to show not just a small change in the average, but a change in weather dynamics, or the concentration of the change in an area where it will make a difference.
In most places in the USA a 1 degree shift in average temperature can result from driving a short distance. In New England it might be the next town over. That kind of local change does not create significant changes in ordinary life.