Is there some data about how many languages exist with or without a writing system? Etnologue enumerates about 6800 living languages and for each language it registers writing systems the language uses, so it might contain the number. Are there any other estimations?
Ethnologue actually provides an answer to this question, although it raises more questions.
The Ethnologue page How many languages in the world are unwritten says that as of the 19th edition (released 2016), there were 7,097 living languages and that of these there is data suggesting that 3,748 have a 'developed writing system'. This leaves 3,349 that are 'likely unwritten'.
No explanation is given as to what is meant by a 'developed writing system' however we can make an informed guess that it refers to a writing system that has been developed in order to be of practical use to the speakers. This would typically rule out writing systems used in technical descriptive works (eg by linguists). It is also commonplace that such writing systems have been developed with the involvement of speakers of the language, quite possibly without a linguist or any other outsiders being involved.
Ethnologue goes on to say that in most cases it is not known what level of usage these writing systems have.