The average points accumulated by 6 students is 88.5. They have all attained different points which are whole numbers. The lowest point is 54 while the highest point is 99.
- Find the average points achieved by the 4 students whose marks lie between the highest and the lowest.
- Find the smallest possible second lowest mark among these 6 students.
- Find the largest possible second lowest mark among these 6 students.
(a)
Total points of 6 students
= 6 x 88.5
= 531
Total points of the rest of the 4 students
= 531 - 99 - 54
= 378
Average points of 4 students
= 378 ÷ 4
= 94.5
(b)
To have the smallest possible second lowest mark among the 6 students, the 3rd student to the 6th student must have as high a score as possible and the 2nd student must have the second lowest score among the 6 students.
So the 6th student will have the highest score. The 5th student will have 1 mark will less than 6th student and this pattern continues to the 3rd student.
1st student's score = 54
2nd student's score = ?
3rd student's score = 99 - 3 = 96
4th student's score = 99 - 2 = 97
5th student's score = 99 - 1 = 98
6th student's score = 99
The smallest possible second lowest mark among these 6 students
= 378 - 98 - 97 - 96
= 87
(c)
To have the largest possible second lowest mark among these 6 students, the 2nd student to the 5th student must have as high a score as possible but lower than the 6th student.
So the 2nd student will have the highest possible second lowest score. The 3rd child must have at least 1 mark higher than the 2nd child and the pattern continues to the 5th child.
1st student's score = 54
2nd student's score = 1 u
3rd student's score = 1 u + 1
4th student's score = 1 u + 2
5th student's score = 1 u + 3
6th student's score = 99
1 u + (1 u + 1) + (1 u + 2) + (1 u + 3) = 378
4 u + 6 = 378
4 u = 378 - 6
4 u = 372
1 u = 372 ÷ 4 = 93
93 x 4 + 6 = 378 (Equal to 378)
Largest possible second lowest mark among these 6 students = 93
Answer(s): (a) 94.5; (b) 87; (c) 93
