Is the frequency of written characters much different from spoken ones?
Of course it is. Interjections are far more common in any spoken language compared to its written counterpart. Chinese also consists of many words and phrases that are very formal and rarely spoken.

https://naccl.osu.edu/sites/naccl.osu.edu/files/NACCL-21_Vol._1--Hongyin_Tao--pp._13-27.pdf could be taken as a starting point.

While the ten most common written characters are 的，一，是，不，了，在，人，有，我 and 他, the most spoken ones are 的，是，我，就，不，你，了，那，啊 and 个。

那个 and 啊 stand out in spoken Chinese, as does 你, since written language usually addresses a collective.

嗯 occupies place 2042 in the written frequency list, but position 30 in the spoken. Similar for 吧 and 哦.