No, no statistics for Schengen tourist visa per nationality are published, although few embassies publish their overall processing times. For example Italian one in Doha says 90% in less than 15 days, and all 100% in 69 days, including the extra background check mandatory for some nationalities. Officially you could ask for status check after 15 calender days.
This may help.
All details for indian passport, Doha Qatar embassies:
Spain - called after 13 days, asked more questions, issued visa single entry C type for 15 days, requested was 7 days, validity was 1 month. No application-recieved stamp under visa sticker.
Hungary - did not call at all, applicant checked on 17th day, asked to come & wait, issuef visa after three hours wait, single entry 7 days, valid also for exact 7 days, exact as requested. Application-recieved stamp on passport under visa sticker.
Germany - applied on Thursday, visa issued on Monday, 15 days long single C type, 1 month valud, requested was 8 days. No application-recieved stamp under visa sticker.
Italy - applied Wednesday 1pm, visa collected Thursday 1pm, single C type, 10 days long, requested was 9 days, 20 days valid. No application-recieved stamp under visa sticker.
All these were for same person, in this exact sequence, with gaps of 6-8 months between each trip, and all rules followed as required.
So, a fresh passport with no history, and originating from an geographical area with history of visa abuses, going to take some time. As the visa issued are used properly and in timely manner, embassies start trusting the applicant.
Hope it helps.