The average points accumulated by 6 participants is 87.5. They have all attained different points which are whole numbers. The lowest point is 55 while the highest point is 96.
- 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 87.5
= 525
Total points of the rest of the 4 participants
= 525 - 96 - 55
= 374
Average points of 4 participants
= 374 ÷ 4
= 93.5
(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 = 55
2nd participant's score = ?
3rd participant's score = 96 - 3 = 93
4th participant's score = 96 - 2 = 94
5th participant's score = 96 - 1 = 95
6th participant's score = 96
The smallest possible second lowest mark among these 6 participants
= 374 - 95 - 94 - 93
= 92
(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 = 55
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 = 96
1 u + (1 u + 1) + (1 u + 2) + (1 u + 3) = 374
4 u + 6 = 374
4 u = 374 - 6
4 u = 368
1 u = 368 ÷ 4 = 92
92 x 4 + 6 = 374 (Equal to 374)
Largest possible second lowest mark among these 6 participants = 92
Answer(s): (a) 93.5; (b) 92; (c) 92
