Question 1028398
(a) The first group consisted of 300 students: 
9% of the students scored 5 (27 students) 
42% scored 6 (126 students)
5% scored 7 (15 students)
44% scored 8 (132 students).

The mode is clearly 8, because it was the most frequently appearing score.
 
The median is 6.  To see this, arrange the scores in increasing order.  The median would be the average of the 150th and 151st values, which is clearly 6.

The average score (mean) of the group is 5*0.09 + 6*0.42 + 7*0.05 + 8*0.44 = 6.84.

(b) Let x = # of students who scored 5 ==> 150-x = # of students who scored 7.
==> {{{(5x+7(150-x))/150 = 6.44}}}

<==> 5x + 1,050 -7x = 966

==> -2x = -84

==> x = 42, the number of students that scored 5.