I was thinking it would be interesting to see what day in history had the greatest variance between temperatures around the world. (Example US City1 90°F, US City2 30°F, Greenland City1 60°F, South Africa City1 80°F and so on, including every major location around the world, look at all those temperature readings together and assign it a number to express how varied the data points are. If the variance is low like how it would normally be in September the data points would be bunched up closer together, if the variance is high like it would normally be in July the data points would be more spread out over a greater range.)
My issue lies with quantifying this variance, intuitively I get the feeling there should be some way to do it since you can easily quantify the variance between just two locations but I'm not sure how to deal with the complications created by having >2 data points.
Like if there was a day where the majority of data points end up bunched up together on either extreme, do you count this as a higher degree of variance than a day where the data points are all evenly dispersed from extreme high to extreme low? I get the feeling there isn't necessarily a correct answer that question which makes me wonder if it's even possible to assign a number for the degree of variance when what exactly "variance" means isn't totally clear.
Ultimately I decided I could settle for the day in history where the difference between the hottest temperature on the planet and the coldest temperature on the planet occurring simultaneously was highest, but I've still not yet found this information because I kinda lost the excitement I randomly had when the thought first came to me.
(Algebra might not be the best flair for this, I honestly wasn't sure what to pick lol.)
e: hmmm maybe if there was some objective way to place all the data points in a certain order, like ordering them by latitude would be simple enough, then you could graph them with an x and a y coordinate. the resulting graph would give you something to quantify but it gives me the feeling that whatever I picked to decide the order on the x axis (y would be temperature) was just totally arbitrary, thus invalidating anything you can glean from the graph.