"Some people like sport, others do not."
Translation:Certaines personnes aiment le sport, d'autres non.
"Certaines personnes aiment le sport, d'autres non" is the exact translation of "Some people like sport, others do not", you mean there are two cases but you don't know how much they are in each case.
"Quelques personnes aiment le sport, d'autres non" is more "a few people like sport, others do not", you mean that they are two cases and that thay are not a lot in the first one.
The plural of "un autre" is "d'autres". Note that technically, the word "autres" functions as an adjective, and the whole phrase is "d'autres personnes". Recall the rule that the partitive article "des" must become "de" in front of an adjective. So when it is the plural of another [thing] :
- (some) other [things] = d'autres [choses]
On the other hand, "des autres" means de + les + autres, where de is the preposition or is part of an expression that uses "de".
Lastly, if the sentence construction calls for de + des + autres, it becomes d'autres. The combination de + des will always default to de.
- J'ai d'autres idées. = I have other ideas.
- Vous avez d'autres questions à me poser ? = Do you have other questions to ask me?
- Je préfère l'odeur des autres fleurs. = I prefer the smell of the other flowers.
- Il a essayé d'autres chaussures. = He tried other shoes.
- Je parle d'autres pays. = I am talking about other countries.
- Je parle des autres pays. = I am talking about the other countries.