Deck construction varies greatly from format to format, and even counting in formats that are more commonly played competitively with constructed decks (Modern, Standard, maybe Legacy) or limited formats (Sealed, Draft), you will find a great difference in deck lists.
Limited formats have the unique feature that you have to work with which cards you open or pick, meaning that while you might get lucky and draw some mana fixing, it will very likely not be enough to alter your mana base significantly because of it.
This will also largely depend on the edition you're playing with - while for most editions you're not too bad off playing 17 or 18 lands, Kaladesh is an edition where you will be suggested playing only 16 lands, due to the overall lower mana curve and speed of the format, and as far as I've noticed it, this is what highly competitive players actually opted for.
Due to the relatively low chance of building combo decks (due to not all editions featuring combo-enabling cards, as well as you not always drawing them), most Limited decks will have a great number of creatures compared to other nonland cards, as those are able to threaten damage over multiple turns, as compared to an Instant or Sorcery.
Constructed is any entirely different animal. Not only do you get many different decks due to the different win conditions - you also can substitute card types you would normally use with others.
The consensus of comments and the first answer seems to be that lands, other than other card types, do have a recognizeable, repeating amount among decks. I would dispute that, due to the fact that MtG provides many different ways to come by the same resource.
To name an example, while you would normally produce red mana with a Mountain or other land card, you might opt for a Simian Spirit Guide (Creature) or Lotus Petal (Artifact), while other decks may still play the basic land, even for one and the same deck concept.
Another factor is how much mana your cards actually require to cast, and how long you intend to play before you win. Modern Affinity is notorious for dropping large portions of the starting hand into play on the first turn for having many cards that cost no mana to cast, resulting in a land base of 16 or even less lands (such as 12 back in 2011). Whichever conclusions you draw from that, and whichever average number you include it in, you will end up with a number that has nothing to do with reality, as the right number is not the average between 24 and 16 - it's 24 for one deck, and 16 for another.
As for other types, you're just completely entering random number territories. Decks will play their combo pieces, which can be any random card type - they are included because they're a part of a combo and do their job, not because the deck needs an arbitrary amount of a certain card type.
To again name an example, if you look at Splinter Twin deck lists, you will commonly find 4 copies of Splinter Twin, which is an Enchantment/Aura card. It's the key card for this very deck, but even considering adding a set number of Auras to a deck because it works for a single deck is ridiculous, as they make you weak to get "2-for-1-ed", meaning that you lose two cards to a single removal spell, for example. Not just including this card in a deck, but deciding to build entirely around it is what makes the deck strong and playable, but all of this is entirely independent of the card type - what matters is the card function.
I don't think you can create an accurate and purposeful diagram over the entire span of MtG competitive formats or decks. What you can attempt to create such a statistic for an individual format, but that will likely give you an average number with no practical purpose, since after all, you're likely not looking for a diagram with decorative qualities, but one to look at it and say "I should probably play n of that type to be successful", and I do believe such a diagram cannot exist for the entirety of the MtG universe.
Since you mentioned other TCGs in your question, let me also mention that MtG has a lot more formats that any other card game I'm aware of, making the issue of a general analysis even more of a complex dilemma, and the lack of this diversity in other formats may well be the reason that such a simple breakdown is possible for those games, but not MtG.
In this answer, the mentioned formats from my introductionary paragraph are the only ones I even considered - there are other formats played competitively, but not to an extend that makes their mention particularily worthwhile or representitive. Whichever numbers you might come up, once you enter Vintage Two-Headed Giant Commander (a format entirely covered by the official rules, mind you, yet not particularily tournament-viable), you will realize they won't work out even by a long shot.