You can find this information from a language corpus (the exact numbers will differ depending on various aspects of the corpus, such as where the data are from--e.g. mainland China or Taiwan--and what register of language it is, e.g. written news reports vs. movie subtitles).

You also need to distinguish between token frequency and type frequency of the tones; you will get different proportions depending on whether you are interested in token or type frequency.

See Zhang & Lai (2010, Phonology) and Da (2004; http://lingua.mtsu.edu/chinese-computing/) for counts that have already been published.

Thanks much.

Did it also occur to you to check not from occurrences, but from the population of the lexicon? Tone 1 (Yin Ping category) would probably have the greatest number of characters, followed by Tone 2 (Yang Ping) and then probably closer to one another are Tone 3 (Shang) and Tone 4 (Qu). I don't have the exact number from any particular dictionary, but anyone who has tried her hand at writing classical poetry would be able to attest to that. Thus, the figures you give appear to be very surprising to me.

Lian-Hee: that is a good point. Off the top of my head, there are at least three different things we could count when quantifying the "distribution" of tones: 1) the overall number of occurrences (the token frequency; e.g., if 我 occurs 500 times in a corpus then that contributes a count of 500 to the overall count for Tone 3); 2) the number of syllables that have that tone (more like a type frequency; e.g., 是、事、市 etc. together still only contribute a count of 1 because they all are pronounced shi4); and 3), what you suggested, the number of characters that have that tone (another sort of type frequency; here, 是、事、市 each contribute 1, so the ≈80 different characters with the pronunciation shi4 would, all together, contribute a count of ≈80 to the overall count for Tone 4). [I'm sure you are already familiar with these and more, but am just spelling it out a little for the sake of other readers who may stumble across this thread.]

Zhang & Lai (2010) report the measures (1) and (2) [based on data from Da Jun's corpus]. For (3), I checked SUBTLEX-CH just now. Perhaps not surprisingly, the ranks come out different each way you count (in each one below I'm listing from T1 to T4, in order)

1) Token frequency (from Zhang & Lai [2010], based on Da [2004]): 16.7%, 18.4%, 14.8%, and 42.5% of the corpus

2) Syllable type frequency (from Zhang & Lai [2010], based on Da [2004]): 258, 224, 254 and 318 syllables

3) character/morpheme type frequency (based on SUBTLEX-CH [Cai & Brysbaert, 2010]): 1366, 1260, 878, 1722

In short: Tone 4 is the most frequent no matter how you slice it (at least in the corpora and methods that I have looked at above), but the ranking of the other three depends on the kind of count and maybe on the corpus.

Stephen, that's really cool stuff! Thanks. 

Thanks much, to the two people who responded, and welcome to others who are thinking about it.

Thanks Lloyd. Well, thanks for the note but Mandarin is not that new to me. ..

I'm an older MA student and Mandarin has been with me for A LONG TIME [but as they say huo3 dao lao3 xue2 dao4 lao4 [Learning it goes on forever]. ..

The various tone systems have variations to be sure -- what I'm interested in looking at is the standard variety [ies] of Mandarin at first. ..

Even trying to identify the standard variety can be difficult and at some point one just needs to pick something, describe the sample, and then analyze it.

There is a big difference between northern and southern Mandarin. The difference does not make them separate languages but it does appear to be big enough to motivate to want to identify separate groups of samples.

Cantonese, Fukienese, Shanghainese, and the other types of Chinese are separate languages and would be very interesting to look at too, eventually. ..

The Mandarin tone system is probably the best to start with because it is relatively uncomplicated. ..I am thinking about selecting some sample of northern Mandarin, probably something from a broadcasting corpus. .. and then develop some benchmark statistics from, say, a sample of, say, exactly 1000 spoken syllables that were actually broadcast. ..

My thinking is to develop a set of benchmark statistics from such a well-defined sample. ..

I could use the set of benchmarks later. ..

I am aware of a very strong prescriptivist and pedagogical quality that exists out there  [for any and every language on earth, probably] but I am trying to stick to a purely natural descriptivist position.

OK thanks

I'm not sure it would be very effective to teach tones one at a time in some order based on their frequency. Tones serve to make contrasts, so I suspect the only way a student will really acquire a tone is to understand how it's different than the other tones (that was the case in my own learning). Thus, I suspect that acquisition would be more successful if students are exposed to all the tones together so they can learn how they sound different and are produced differently (although I'm not aware off the top of my head of any research empirically testing this prediction). Trying to teach one tone at a time would also severely limit what vocabulary you have available to expose the students to.

Training specific contrasts, like you suggested, sounds potentially more useful; I'm not aware of specific studies testing that but they might exist. A good starting point for the L2 tone training literature is Wang, Jongman, and Sereno (I think 2001 or 2004, somewhere around there).