Will downloading IOS 9 delete the storage that iOS 8 took up?

I have a 16gb iPhone 6, and it come with iOS 8, and I only had 11.6 gb to work with as soon as I got the phone with all of the software installed. My question is: will downloading iOS 9 delete the iOS 8 data, thus freeing up more space after the download because iOS 8 took up more storage?

It will replace OS 8

Yes.