I agree with jzd: it will be hardly possible to collect those statistics. Who is an average user? What is freeware? etc.
Moreover, reading the comments, I see that you are asking the question to evaluate the reason to create a freeware product or not. I quote your comment:
It is very relevant if you consider whether to create freeware or not. If the answer to this question was that the average computer has 0.0001 freeware installed then it is probably not a good idea to develop something and release it as freeware.
Well, it's not. When an "average user" installs something on her computer, it's not just because it's freeware. It's because it is something she needs or wants to install. By reducing your consideration to a sole aspect of price, you forget that it's not because your application will be released freeware that it will be downloaded at all.
- Adobe Photoshop is used a lot (including legally) because it's a high-quality software product, even if it costs thousands of dollars.
- Firefox is a huge success because it's a fast, high-quality browser which is very extensible, and is also free.
- Internet Explorer is used by a large number of users because it is (was) preinstalled by default on Windows platform.
- The application I wrote two years ago was downloaded 0 times because there was no marketing, because the application is not useful, and because it is crappy and with an ugly design. Even if it's freeware. And even if I'll pay to every user, nobody will download it.
In the same way, the rest of your reasoning seems wrong to me:
If the answer is 20 freeware, then this means that there is such a huge number of users, which uses freeware (compared for example to software) that it might pay off to release something as freeware and possibly live off the support or consuling.
If the answer is 20 freeware, it doesn't mean anything at all. Especially since many users do install lots of applications they do never use lately, or they install applications without even knowing they are installing them.
So create a high quality product which is needed, advertise, and it will be used, independently of the number of freeware applications installed on the average user computer. And to do so, ask the users directly about their needs, rather than how much freeware applications do they install.
If such large and global metric does not mean anything for a specific product, you can instead try to evaluate some more precise things:
- If there are other similar applications which are also freeware, are they downloaded a lot? If not, why? If yes, how you will compete with them?
- If there are other similar applications which are paid, do they have a lot of users? Are those users angry to pay for those apps? If yes, why?
- In general, what actual products miss that you can bring with your product? If there are freeware products whose quality is low and their users want a more high quality freeware product, it's not exactly the same thing as if there are paid products whose quality is high but the users don't want to pay for them and are ready to use a freeware version with less features.