The average points accumulated by 6 pupils is 90.5. They have all attained different points which are whole numbers. The lowest point is 69 while the highest point is 100.
- Find the average points achieved by the 4 pupils whose marks lie between the highest and the lowest.
- Find the smallest possible second lowest mark among these 6 pupils.
- Find the largest possible second lowest mark among these 6 pupils.
(a)
Total points of 6 pupils
= 6 x 90.5
= 543
Total points of the rest of the 4 pupils
= 543 - 100 - 69
= 374
Average points of 4 pupils
= 374 ÷ 4
= 93.5
(b)
To have the smallest possible second lowest mark among the 6 pupils, the 3rd pupil to the 6th pupil must have as high a score as possible and the 2nd pupil must have the second lowest score among the 6 pupils.
So the 6th pupil will have the highest score. The 5th pupil will have 1 mark will less than 6th pupil and this pattern continues to the 3rd pupil.
1st pupil's score = 69
2nd pupil's score = ?
3rd pupil's score = 100 - 3 = 97
4th pupil's score = 100 - 2 = 98
5th pupil's score = 100 - 1 = 99
6th pupil's score = 100
The smallest possible second lowest mark among these 6 pupils
= 374 - 99 - 98 - 97
= 80
(c)
To have the largest possible second lowest mark among these 6 pupils, the 2nd pupil to the 5th pupil must have as high a score as possible but lower than the 6th pupil.
So the 2nd pupil 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 pupil's score = 69
2nd pupil's score = 1 u
3rd pupil's score = 1 u + 1
4th pupil's score = 1 u + 2
5th pupil's score = 1 u + 3
6th pupil's score = 100
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 pupils = 92
Answer(s): (a) 93.5; (b) 80; (c) 92
