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Average?
The hottest place on earth is the core, about 4400°C to 6000°C(average around 5200°C)
https://education.nationalgeographic.org/resource/core/
A short google point out that the coldest place on earth is Eastern Antarctic Plateau, Antarctica (-94°C)
https://www.newscientist.com/question/coldest-places-earth/#:~:text=1)%20Eastern%20Antarctic%20Plateau%2C%20Antarctica,of%20coldest%20place%20on%20Earth.
And since no living thing is hotter than earth core and no living thing is colder than antarctica(other than my ex), then we calculate the average of this two((5200 + -94)÷2) and we get 2553°C. That's the average temperature of earth.
That's a pretty dumb way of calculating average since it's just the average of the biggest value and the smallest value. That's neither mean, median, or mode for the whole planet. It needs to be weighted by volume or mass in order to be an accurate average.
It is a half decent Fermi approximation though.
I mean OP asked for average, that's how average calculated 🤷
Median is impossible to calculate since you need a whole array of data to know what's in the middle. I think anything other than that is impossible because we need gazillion of data to even getting close to the accurate answer, that's why all answer out there is usually categorised and in estimate.
That's not how average is calculated, that would be the average if there were two particles, one 5200 and one -94. The average is the sum of all values divided by the number of values. Not the max plus the min divided by 2.
If only there were some extensive property of matter we could multiply with the temperature to compute a weighted average. That would be massively helpful.
OP has also asked for meaningful