Ms. Davis gave a quiz to her class of $15$ students. The dot plot below shows the distribution of quiz scores.

Later Ms. Davis discovered that there was a grading error on one of the questions. She regraded the quizzes, awarding some of the students $10$ extra points, which increased the median quiz score to $80$. What is the minimum number of students who received extra points?
(Note that the median quiz score is the middle score if the $15$ quiz scores are arranged in increasing order.)