Just to show off, in Java version 12 (preview enabled), using the new Switch Expressions:
String grade = switch(avg/10) {
    case 9,10 -> "A";
    case 8    -> "B";
    case 7    -> "C";
    case 6    -> "D";
    case 5    -> "E";
    default   -> "F";
};
or, very flexible, if not being to lazy:
String grade = switch(avg) {
    case 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 -> "A";
    case 80, 81, 82, 83, 84, 85, 86, 87, 88, 89      -> "B";
    // you got the idea, I AM lazy
Real (?) solution: use NavigableMap (example TreeMap) with its floorEntry() or lowerEntry() methods:
NavigableMap<Integer, String> grades = new TreeMap<>();
grades.put(90, "A");
grades.put(80, "B"); 
...
// usage
String grade = grades.floorEntry(avg).getValue();
values in map must eventually be adjusted