The average points accumulated by 6 pupils is 83.5. They have all attained different points which are whole numbers. The lowest point is 59 while the highest point is 92.
- 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 83.5
= 501
Total points of the rest of the 4 pupils
= 501 - 92 - 59
= 350
Average points of 4 pupils
= 350 ÷ 4
= 87.5
(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 = 59
2nd pupil's score = ?
3rd pupil's score = 92 - 3 = 89
4th pupil's score = 92 - 2 = 90
5th pupil's score = 92 - 1 = 91
6th pupil's score = 92
The smallest possible second lowest mark among these 6 pupils
= 350 - 91 - 90 - 89
= 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 = 59
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 = 92
1 u + (1 u + 1) + (1 u + 2) + (1 u + 3) = 350
4 u + 6 = 350
4 u = 350 - 6
4 u = 344
1 u = 344 ÷ 4 = 86
86 x 4 + 6 = 350 (Equal to 350)
Largest possible second lowest mark among these 6 pupils = 86
Answer(s): (a) 87.5; (b) 80; (c) 86
