While there is no preexisting information to fully complete the data requested, I used the available facts to pull together the number of schools that offer General Certificate of Secondary Education (GCSE) examinations in the UK (excluding Scotland); the number of students who took the examinations; and the average number of qualifications earned per student.
By definition, the GCSE exam is: "An examination set especially for secondary-school pupils of 16 years of age in England, Wales, and Northern Ireland", as per the English Oxford Dictionary. After scouring trough the websites of several education establishments, online learning platforms, dictionaries, educational websites, and examination boards (such as Ofqual, Qualifications Wales, and CCEA), I was able to confirm that in fact GCSEs are only taken in the United Kingdom, as well as the fact that they are not available in Scotland, where pupils sit for "Standard Grade" exams instead.
Below you'll find an outline of my research methodology as well as a deep dive into my findings. Again, considering that the nature of the GCSE exams is to grade students in England, Wales and Northern Ireland, the information you've requested for Europe (excluding UK), Middle East, Africa, Asia, North America and South America is nonexistent therefore not included in the attached spreadsheet. Additionally, please note that every future reference to "United Kingdom" is to be understood as England, Wales and Northern Ireland. Since the GCSE examinations are not offered in Scotland, the country was excluded in all statistics and data corresponding to the United Kingdom.
Finally, the latest information I could find in the websites of education establishments; news sources; examination boards such as Ofqual, Qualifications Wales, and CCEA; and Government-issued reports concerning England, Wales, and Northern Ireland corresponds to 2016.
I concluded that 768,353 students took GCSE examinations in the United Kingdom. The exams were offered in 5,538 schools and the average number of qualifications obtained per student was 6.8.
After extensive research through education establishments' websites; news sources; examination boards's websites, and Government-issued reports, I was not able to find publicly available data for the United Kingdom as a whole.
To get to the number of students who took the GCSE in the UK (768,353), I added the total number of students taking the exam in England (574,130), Wales (32,248), and Northern Ireland (161,975); which led me to a total of 768,353 students taking the GCSE in the UK. You'll find the sources from where I was able to get each of these numbers linked in the name of the corresponding country, below:
England = 574,130
Wales = 32,248
Northern Ireland = 161,975
Total UK students = 768,353
Secondly, to find the total number of schools offering the exam in the UK (5,538), I added the number of schools offering them in England (5,134), Wales (210), and Northern Ireland (194); which results in a total of 5,538 schools offering the exam. You'll find a link to the source for each of these quantities for the corresponding country below, as well as a more detailed explanation on how I got to the England data.
England= 5,134 *
Wales = 210
Northern Ireland = 194
Total number of UK schools = 5,538
* To get to this number, I researched the number of schools that had students who took the GCSEs in England in 2016 through the Government's website.
Finally, to get to the average number of qualifications obtained per student, I researched the total number of qualifications taken in the UK. This was reported by the BBC to be 5,240,796. I divided this total number of qualifications by the total number of students who took the exam in the UK (768,353, as detailed by my calculations above). This resulted in a 6.8 average number of qualifications per student in 2016.
5,240,796/768,353 = 6.8.
To wrap up, an average of 6.8 GCSE qualifications were obtained by 768,353 students, who took the examinations in 5,538 schools in the UK (excluding Scotland, which has different qualifications). This information was added in the corresponding cells of the attached spreadsheet.
Since the GCSE examinations are only available in the England, Wales, and Northern Ireland, the information requested does not exist for Europe (excluding UK), Middle East, Africa, Asia, North America and South America. An international version of the GCSE (IGCSE) was introduced around 25 years ago so that students overseas could take the exam.