The film industry has an adminstrative position called Line Producer. They deal with managing team schedules, the project budget, making sure resources are available for the team, booking / chairing meetings, and dealing with paperwork, clients and upper management. This sounds like an equivalent position but without the (less professional sounding in my opinion) buzzword compliant "Scrum Master" moniker.
The actual task of getting the project done falls to a Supervisor (ie a project manager) who deals with technical and creative decisions, assigning tasks to the team, and critiquing work in progress.
A female Line Producer often work very well when dealing with a mainly male team. This could be to do with fewer ego clashes and women generally being more organised (again my personal opinion).