I did the same thing you did ... I added up the "scores" column
and divided the total by 5 . That answer is 2 .
Then I read what you said about the answer sheet, so I went back
and looked at the problem again. Good thing I did. You have to look
and see what the first column says, and what it means.
There are FIVE different students who each scored 4.
There are THREE different students who each scored 3.
There are FOUR different students who each scored 2.
.
.
etc.
The total of all the scores is 44, not 10.
The total number of students is 20, not 5.
That's where the "2.2" comes from.