I assume you store the singer as a key, and the popularity (of the singer) as value. A HashMap is not ordered, and a TreeMap is ordered by key, not by value, so it won't help.
If you need your singers ordered by popularity, then build a list with all the singers in the map, and then sort this list using a comparator which compares the popularity of both singers:
List<String> singers = new ArrayList<String>(map.keySet());
Collections.sort(singers, new Comparator<String>() {
@Override
public int compare(String s1, String s2) {
Integer popularity1 = map.get(s1);
Integer popularity2 = map.get(s2);
return popularity1.compareTo(popularity2);
}
});