Question 1028398: Two groups of students took a certain test with possible scores 1,2,3,4,5,6,7,8,9,10.
(a) The first group consisted of 300 students; 9% of the students scored 5, 42% scored 6, 5% scored 7 and the remaining 44% scored 8. Calculate the average score of this group. Also, calculate the median and the mode.
(b) A second group of 150 students also took the test. The only scores this group of students obtained were 5 and 7. The average score was 6.44. How many students scored 5 for the test?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! (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 + 1,050 -7x = 966
==> -2x = -84
==> x = 42, the number of students that scored 5.
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