I read this sentence :
The three individuals are so different that their tastes vary from one another's.
In this their tastes are compared so apostrophe is used with another
But in this sentence
She was not a good singer but she danced better than any of us.
Why did or something like that has not been used ? Like previous sentence in which their tastes is compared here their dance is being compared.
I think the key here is that the first sentence uses "taste" as a possessive noun. The word another can be used as another's in the possessive form, which is known as a fused head construction [1]. Example:
These two imparadised in one another's arms.
The second sentence uses dance as a verb and not a noun, which means the same rules do not apply here. However, you can get close to the first sentence by using dance as a possessive noun, such as :
She was not a good singer, but her dance was better than any of ours.
Or
She was not a good singer, but none of our dance was as good as her's.
[1] https://en.m.wiktionary.org/wiki/another
Helpful read : http://www.grammar.com/fused-participle-noun-or-pronoun-and-%E2%80%91ing-phrase/
