The document describes a class of 12 students where: - The lowest quartile average is 40 - The middle third average is 60 - The highest quartile average is 80 - The 4th student scored 70 - The top 3 students scored the same (80) - The last 3 scores are in arithmetic progression Using the above information and the overall class average of 62, the individual scores of 6 students can be determined.

1. Averages

2. Averages
Average mark of the lowest quartile of a class of 12 students is 40.
Average mark of the highest quartile is 80. Average score of the
middle one-third is 60. The person who stood 4th scored 70. The
overall average score is 62. Furthermore, we are told that the top 3
scored the same mark, and the score of the last three students is in
AP. How many individual scores do we know of the 12 people?
(a) 6 (b) 5
(c) 7 (d) 2

3. Averages
Highest Score-
Lowest Score-
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12

4. Averages
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12
- Lowest quartile : Average = 40
- Middle one-third : Average = 60
- Highest Quartile : Average = 80

5. Averages
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12
- Average = 40
- Average = 60
- Average = 80
- Score of the 4th student = 70

6. Averages
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12
- Average = 40
- Average = 60
- Average = 80
- Score of the 4th student = 70
Top 3 students scored
the same marks. thus,
they scored 80 each.

7. Averages
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12
- Average = 40
=>a-11 = 40
- Average = 60
- Average = 80
- Score of the 4th student = 70
The last three digits are
in A.P, Thus the middle
term is equal to the
average of the three
numbers.
So, a-11 = 40

8. Averages
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12
- Average = 40
=>a-11 = 40
- Average = 60
- Average = 80
- Score of the 4th student = 70
The average of all 12
numbers is given, from
which the sum of 12
numbers could be
found. Then the sum of
the remaining 11
numbers could be
found from averages.

9. Averages
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12
- Average = 40
=>a-11 = 40
- Average = 60
- Average = 80
- Score of the 4th student = 70
Thus, by subtracting
the sum of 11 numbers
from the total of 12
numbers, the value of
a-9 can be found to be
74. Explained by below
equation.
80*3+70+60*4+40*3
+ (a-9) = 12*62

10. Averages
a-1
a-2
a-3
a-4
a-5
a-6
a-7
a-8
a-9
a-10
a-11
a-12
- Average = 40
=>a-11 = 40
- Average = 60
- Average = 80
- Score of the 4th student = 70
Thus, We know the
individual scores of
6 people out of 12.
Answer Choice (A)

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