Also, you don't need to count how many cards are in your deck. Order them by cost (cheapest at bottom). Then cut your deck roughly in half, and flip over the cheaper half. Now one pile has your cheapest card on top, the other your most expensive. Now just start discarding equal numbers of cards from each pile, say in chunks of four since can recognize that number intuitively without counting. Keep doing this until one pile is empty. Now your median cost is the median cost of what is left, which ought to be small enough to just fan out and see the median readily.
This is basically counting but without keeping track of the number - I don't see how it's better.
On the other hand, gardens makes you count your deck, and it's not big problem. Philosopher's stone also exists.
Anyway, I would definitely say no to median (or mean) of your deck; basically, it makes you have to keep track of every single card you have in your deck to know how much it is worth, and that doesn't sound like fun game to me.
It's better than counting because if someone screams "the chicken is burning" and you have to go extinguish it, and come back, you don't need to keep a number in your head when you come back to finish counting. That's an issue for me, except it is more like ADD thoughts than actual distractions.
You don't
have to keep track of every single card in your deck, it will just give you an advantage to do so, and it increases that advantage more than the edge it already gives you in official Dominion. Wishing Well and Mystic are out there though. I feel like if you're a casual player, you'll just kind of wing it and maybe sometimes it will end up being worth 4 when you were hoping for it to be worth 5, and you say, oh poo. If you're a competitive player, you're probably looking at a goko log anyway. I personally find Wishing Well more distasteful, playing a Wishing Well, leaving one card left in the deck, and naming the wrong card makes me feel pretty depressed, and at the same time doing the deck tracking necessary to make the hit hurts my head.