One way, which is less private, show active installs by having the phone reports
back to the store if it's unstalled
A more secure way, show downloads for each version/build. Graph it. If an app is releasing/being updated regularly but more users are uninstalling, you'd expect the downloads per version to decrease or stay level
If you install it once and then remove it, you only do a single download. If you install it and keep it installed for several app updates, you download it for every update. If a lot of people download it at the same time due to an app update, you'll see a huge download spike immediately after a release.
It's a very rough metric, but it could be added without adding any kind of additional telemetry to the client, and it would give at least a small hint of what's happening.
