The average points accumulated by 6 participants is 86.5. They have all attained different points which are whole numbers. The lowest point is 63 while the highest point is 94.
- Find the average points achieved by the 4 participants whose marks lie between the highest and the lowest.
- Find the smallest possible second lowest mark among these 6 participants.
- Find the largest possible second lowest mark among these 6 participants.
(a)
Total points of 6 participants
= 6 x 86.5
= 519
Total points of the rest of the 4 participants
= 519 - 94 - 63
= 362
Average points of 4 participants
= 362 ÷ 4
= 90.5
(b)
To have the smallest possible second lowest mark among the 6 participants, the 3rd participant to the 6th participant must have as high a score as possible and the 2nd participant must have the second lowest score among the 6 participants.
So the 6th participant will have the highest score. The 5th participant will have 1 mark will less than 6th participant and this pattern continues to the 3rd participant.
1st participant's score = 63
2nd participant's score = ?
3rd participant's score = 94 - 3 = 91
4th participant's score = 94 - 2 = 92
5th participant's score = 94 - 1 = 93
6th participant's score = 94
The smallest possible second lowest mark among these 6 participants
= 362 - 93 - 92 - 91
= 86
(c)
To have the largest possible second lowest mark among these 6 participants, the 2nd participant to the 5th participant must have as high a score as possible but lower than the 6th participant.
So the 2nd participant 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 participant's score = 63
2nd participant's score = 1 u
3rd participant's score = 1 u + 1
4th participant's score = 1 u + 2
5th participant's score = 1 u + 3
6th participant's score = 94
1 u + (1 u + 1) + (1 u + 2) + (1 u + 3) = 362
4 u + 6 = 362
4 u = 362 - 6
4 u = 356
1 u = 356 ÷ 4 = 89
89 x 4 + 6 = 362 (Equal to 362)
Largest possible second lowest mark among these 6 participants = 89
Answer(s): (a) 90.5; (b) 86; (c) 89
