Notice on page 7 the author briefly alludes to weighted means. That part is very useful to programmers & data scientists. If you build up good intuition about h

Notice on page 7 the author briefly alludes to weighted means. That part is very useful to programmers & data scientists. If you build up good intuition about how to choose those weights, you can use them for all sorts of programming/networking/graphics problems. For example - suppose you host some data on 3 cloud providers - GCP, AWS & Azure. You believe, on average, the latency is the same for each provider. However, the variance is different - say 2,3 and 4. So, how much traffic should you route to each provider ? "What does the mean really mean" is the same as the above question. If you believe average latency is the same, then how should it matter what the variance is ? Just route 1/3 of your traffic to each provider & be done. But that's exactly the wrong answer! Because the arithmetic mean is not what you want here. You want to make your own mean. You really want a weighted mean, but you can't just pick the weights willy-nilly. The sample mean has its own variance! So if you say you don't give a rat's ass about statistics, you will just route 1/3 traffic to each provider - what you are really doing is picking weights of 1/3, in turn giving your sample mean xbar a sample variance of exactly 1 ( easy to show ). But if you pick the right weights, the sample variance drops to 12/13, which is smaller than 1. So by picking your own weighted mean, you get to fiddle with the sample variance - you can dial it up or down! The smallest you can get it down to is 12/13, in which case the weights will have to be 6/13 to GCP, 4/13 to AWS & 3/13 to Azure. Fun stuff.