The iOS app store doesn't show download figures, not even the vague ranges shown on Google. Is there a source to obtain download stats for various apps on iOS?
No. However there are a number of services that analyze Appstore data and attempt to guess the number of downloads for specific apps and categories. Most of the detailed information is pay-only, keep in mind for iOS apps, this is all based on guesswork since Apple does not release detailed data for the entire store.
http://appannie.com
http://www.statista.com
https://prioridata.com
For the education (free) category, an app that I worked on reached the top 25 with ~1,000 downloads a day. The bar is higher now across the board.