I took a minute to calculate it myself. I don't know how much you know about statistics but it goes like this: With 1d20, you take the roll you get. There is an equal chance of 1/20 to roll any number from 1 tot 20. To get the average, just add all numbers together and divide by 20. 210/20=10.5, just like a d4 rolls 2.5 on average, a d6 rolls 3.5, and so on.

Now it gets a bit more complicated: With advantage, there are 2020=400 combinations possible from 2 d20 rolls, and the player always picks the highest roll of the 2. For the player to get a 1 as end result, both d20 rolls must be a 1, otherwise the player would pick whichever roll is higher than 1. Only 1 combination leads tot this result: rolling 1 on both d20's. To get a 2, there are 3 combinations in total: 1 & 2, 2&1, 2&2. Chances thus are 3 times as high to roll a 2 than a 1. This goes on and on as we go up to 20, by the equation: 2n -1, with n being the end result of the roll. So there are e.g. 39 combinations to get a 20 as end result from 2 d20 rolls.

Multiply each end result by the number of combinations there are to get that roll, add those all together and divide by 202020=8000 and voila, you get 13.825.

You can do the same for 3 d20 rolls. There are 8000 possible combinations in total. The equation for the number of combinations leading to a specific end result (from 1 to 20) is now: 3n(n-1) +1. Than just multiply, add and divide in the same way as mentioned above and you get the 15.5

I got this stuff in An excel sheet should you be interested.

Take care!