The average points accumulated by 6 students is 86.5. They have all attained different points which are whole numbers. The lowest point is 70 while the highest point is 95.
- 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 86.5
= 519
Total points of the rest of the 4 students
= 519 - 95 - 70
= 354
Average points of 4 students
= 354 ÷ 4
= 88.5
(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 = 70
2nd student's score = ?
3rd student's score = 95 - 3 = 92
4th student's score = 95 - 2 = 93
5th student's score = 95 - 1 = 94
6th student's score = 95
The smallest possible second lowest mark among these 6 students
= 354 - 94 - 93 - 92
= 75
(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 = 70
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 = 95
1 u + (1 u + 1) + (1 u + 2) + (1 u + 3) = 354
4 u + 6 = 354
4 u = 354 - 6
4 u = 348
1 u = 348 ÷ 4 = 87
87 x 4 + 6 = 354 (Equal to 354)
Largest possible second lowest mark among these 6 students = 87
Answer(s): (a) 88.5; (b) 75; (c) 87