Is there a ratio of the number of wizards living in a certain country compared to the number of muggles living there?
For example, in the 1990-1998, The United Kingdom's muggle population was 57-59 million, what would the wizarding population of the United Kingdom have been?
The rest of the world?
USA MUGGLE POPULATION 1990-1998- 250-273 million
FRANCE MUGGLE POPULATION 1990-1998- 58.5-60 million
In answer to the first part of your question, there isn't a vast amount available on this but J. K. Rowling's writing on the history of magic in America specifically says:
The overall ratio of wizards to non-wizards seemed consistent across populations
History of Magic in North America Part One
As for specific calculations, I would refer you to this exceptionally detailed answer: What is the total population of wizards?
Many people have tried to answer this question before, but it is very tricky, simply because a lot of information contradicts itself. For example, Rowling once said that for every 10 Muggles there is one wizard, but that would not make sense, given the fact that the population would be around 6 million. And considering that there is only one Wizarding school in the UK, which is Hogwarts. Harry's year has just 40 in the year, although that may have been very low compared to the average.
I am going to try and calculate it by using the number of kids at Hogwarts. So let's say there are 100 per year, that would mean 700 in the school at any given moment. It is said that Wizards live on average to 137 years (seems logical considering that there is a spell that will cure almost every illness). You can find the fraction of time a Wizard would spend at school (dividing 137 by 7) is 5 percent of thier life on average. And if there are 700 in a school then you can multiply it by 20 to get 2100 wizards in Britain, so that would be one Wizard for every 27,000 Muggles.
simplify the math- if there are 100 per year and a lifespan of 137 years that would be 13700 wizards and witches. Also 700 times 20 would be 14000 wizards, not 2100. between 57 and 59 million muggles in England at the time would mean over 4,000 and under 4500 muggles per wizard, if a) the average class size is 100 b) Hogwarts is in fact the only wizarding school in England, c) all wizards go to school, and d) there are the same number of English wizards studying abroad as there are foreign wizards studying at Hogwarts. On the wiki it states "Smaller and less well-regulated institutions were rarely registered with the appropriate Ministry and are difficult to keep track of" There is also the strong indication that most wizards worldwide do not receive a formal education, meaning the number of muggles per wizard will be much lower. The other question, of course, is how the squibs are calculated into this- they may well be counted as part of the wizard population but not receive a formal education that they would find useless. Also note that Uagodou is the largest school in the world, covering all of Africa (muggle pop. 1.29 Billion) which if this were at the 10:1 listed ratio would be 130 million witches and wizards or roughly 1 million students per class. Also of question is whether the official wizarding population includes entities such as house elves which are classified as people though they are clearly unable to attend the school as students.
