Try to look at this non-academic publication

http://images.forbes.com/forbesinsights/StudyPDFs/global_diversity_rankings_2012.pdf

You may also try this website:

http://www.nationmaster.com/

I have also done some research on accommodating for ethnic diversity in education that might be of interest to you.

Best regards,

Debra

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Dear Nezahat

Let me propose two interesting global database.

The first one (and the most interesting, in my humble opinion) is the Human Relations Area Files (http://hraf.yale.edu/). It is based on an "anthropological" approach (very useful if you look at what you call "cultural or ethnic diversity"). But it is not free...

The second one is Ethnologue (https://www.ethnologue.com/). It is based on a linguistic approach (so, it take into account only "linguistic diversity"). But it is free.

Obviously, none of them is a "perfect" tool, but a crossed research will help you to identify the data you need about cultural and ethnic diversity for country/region/continent.

I hope that info may be useful.

Best wishes,

mao

http://hraf.yale.edu/

https://www.ethnologue.com/

Try the CIA's world fact book.

https://www.cia.gov/library/publications/the-world-factbook/

If your are interested in the process of Unity from Dversity, look at - http://wpf-unesco.org/

Dear Nezahat,

please have a look into 

https://www.cia.gov/library/publications/the-world-factbook/fields/2075.html

For more systematic data collection, for official versus nongovernmental research,  I found going to each country Census  pages, a fascinating read.

I have attached an example of NZ census

you can see this link, it may be useful to yuo

https://www.researchgate.net/deref/http%3A%2F%2Fimages.forbes.com%2Fforbesinsights%2FStudyPDFs%2Fglobal_diversity_rankings_2012.pdf

Could you fine tune your definition of "CULTURAL or ETHNIC DIVERSITY by countries"? Do you mean how much diverse countries are, or do you seek the actual composition of this diversity? Some countries (like France) forbid any collection of such data so I don't know what international data are worth. 

Dear Nezahat:

Perhaps the following link to the Pew Research Center could be of your interest:

http://www.pewresearch.org/fact-tank/2013/07/18/the-most-and-least-culturally-diverse-countries-in-the-world/

Good luck!!!

Dear Nezhart;

Please follow the Hofstede centre, it is operated by itim International, a network based consultancy with the endorsement of Prof Geert Hofstede on the field of the Cultural dimension theory, Hofstede conducted one of the most comprehensive studies of how values in the workplace are influenced by culture.

For more detailed, see the following link and maybe they could be of your interest:

https://geert-hofstede.com/countries.html

Best regards

https://geert-hofstede.com/countries.html