The most difficult for me in learning Chinese is memorizing the correct tone.
I tried to find on web what the most frequently used tones are, but it seems to be hard to find.
I suppose if one tone is used 50 % of the time, I will just need to memorize the other ones. For instance tone 4 seems to be very frequently used, and I will just have to memorise perfectly tones 1, 2 and 3.
I did some searching for tone distribution chinese and found this post ("What is the distribution of tones in Mandarin Chinese?") on Quora.
One person who responded took a list of characters and extracted, with some programming, the tone(s) for each character. (Multiple pronunciations are permitted and counted separately.) The result he got was:
However, I am not sure what exactly was counted as a "word".
More importantly, there is also the presence of a tone sandhi. This allows for a "neutral" tone (e.g. in 妈妈) and in a sequence of two repeated third tones, for the first third tone to shift to a second tone (e.g. in 你好). (There are also some more examples with the behaviour of specific characters.) As a result, working off of dictionary entries may not reflect actual frequencies of tones, and moreover, the specific tone used will depend on context.
In any case, this and my experiences with Chinese indicate that there's no one tone that comes up overwhelmingly frequently. However, there are some pointers in this question for tone memorisation, and I particularly like the idea here.
Even more useful than learning the individual tones is their learning their combinations.
One combination many English-speakers seem to have trouble with is 3 + 2, as in
etc. This combination is particularly useful because it helps people grasp the correct sound of both tone 2 and tone 3, by juxtaposing them and so highlighting their differences.
The advantage of learning all 4 * 5 = 20 combinations reasonably well is that each two-syllable word you know serves as a model for new words that have the same pattern.
