Pew Research Center

A Recent Survey conducted by the Pew Reserch Center in the USA names "Library Services in the Digital Age" is focused on the unusual programs and activities not typically associated with libraries that it tends to overlook the mere provision of a peaceful place to read and think. Nevertheless, the parts of the report dedicated to what people really want from their libraries makes the public’s wishes clear.
The two services that patrons regard as most essential in a library are “librarians to help people find information” and “borrowing books,” each rated as “very important” by 80 percent of respondents. Next comes “free access to computers and the Internet,” rated very important by 77 percent of those surveyed. No surprises there. These three services are what nearly everyone has come to regard as a public library’s core mission.
“Quiet study spaces for adults and children” comes in fourth, and here is where the results go rogue. The percentage of people who consider quiet spaces to be a very important element in any public library is 76, only one percentage point less than the value given to computer and Internet access. A relatively silent place to read is almost exactly as valuable to these people as the Internet!

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Further reading
“Library Services in the Digital Age” by Kathryn Zickuhr, Lee Rainie and Kristen Purcell at the Pew Internet & American Life project