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The graph below shows few students distribution of quiz scores a teac
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18 Dec 2023, 01:03
18 Dec 2023, 01:03
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The graph below shows few students’ distribution of quiz scores a teacher recorded for a quiz consisting of 10 questions. Each question was worth one point.
GRE quiz.jpg [ 33.34 KiB | Viewed 1624 times ]
After recording the scores and knowing that question number ‘2’ was incorrect, the teacher decided to give full credit for question number ‘2’ to every student.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Attachment:
GRE quiz.jpg [ 33.34 KiB | Viewed 1624 times ]
After recording the scores and knowing that question number ‘2’ was incorrect, the teacher decided to give full credit for question number ‘2’ to every student.
Quantity A |
Quantity B |
The new mean quiz score of thestudents, considering score forquestion number ‘2’ |
7 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: The graph below shows few students distribution of quiz scores a teac
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18 Dec 2023, 22:37
18 Dec 2023, 22:37
3
The mean quiz score = total sum of the quiz scores / number of students. According to the graph, we find there are 25 students.
Add up the total sum of the quiz scores (prior to the credit given for the incorrect question):
3*2+4*1+5*4+6*3+7*5+8*5+9*3+10*2 = 170
The part about "question number 2" isn't necessary, since regardless of the question number, each student will be given 1 single point additionally to the scores represented in the graph. Therefore, you can add 25*1 points to the total sum for the new total sum, then divide by 25 to find the new mean.
(170+25)/25 = 7.8
Since 7.8 > 7, the new mean quiz score is greater than 7.
Add up the total sum of the quiz scores (prior to the credit given for the incorrect question):
3*2+4*1+5*4+6*3+7*5+8*5+9*3+10*2 = 170
The part about "question number 2" isn't necessary, since regardless of the question number, each student will be given 1 single point additionally to the scores represented in the graph. Therefore, you can add 25*1 points to the total sum for the new total sum, then divide by 25 to find the new mean.
(170+25)/25 = 7.8
Since 7.8 > 7, the new mean quiz score is greater than 7.
Re: The graph below shows few students distribution of quiz scores a teac
[#permalink]
20 Sep 2025, 23:59
20 Sep 2025, 23:59
To solve this problem, we determine the relationship between the new average quiz score (after giving full credit for question 2 to every student) and 7 by analyzing data uncertainty and the rule for question 2.
The quiz has 10 questions, each worth 1 point (full score 10).
There are 25 students.
Original total score: 3×2 + 4×1 + 5×4 + 6×3 + 7×5 + 8×5 + 9×3 + 10×2 = 170 .
2 students originally got full marks (10 points), meaning they already got 1 point for question 2 (else no full marks).
For the remaining 25 - 2 = 23 students, it's uncertain if they got points for question 2 originally (due to "question 2 being incorrect").
The teacher gives full credit (1 point) for question 2 to every student:
2 full-mark students: Scores stay 10 (already have question 2's 1 point).
23 other students: Each gets +1 if they lacked question 2's point originally; scores stay same if they had it.
The 23 students can get at most 23 extra points (none had question 2's point) or at least 0 (all had it). So:
Minimum new total score: 170 + 0 = 170 .
Maximum new total score: 170 + 23 = 193 .
Average = total score ÷ 25 students:
Minimum new average: 170 ÷ 25 = 6.8 .
Maximum new average: 193 ÷ 25 = 7.72 .
The new average ranges from 6.8 to 7.72
it can be < 7 or > 7.
The relationship cannot be determined from the given information.
Answer: D
The quiz has 10 questions, each worth 1 point (full score 10).
There are 25 students.
Original total score: 3×2 + 4×1 + 5×4 + 6×3 + 7×5 + 8×5 + 9×3 + 10×2 = 170 .
2 students originally got full marks (10 points), meaning they already got 1 point for question 2 (else no full marks).
For the remaining 25 - 2 = 23 students, it's uncertain if they got points for question 2 originally (due to "question 2 being incorrect").
The teacher gives full credit (1 point) for question 2 to every student:
2 full-mark students: Scores stay 10 (already have question 2's 1 point).
23 other students: Each gets +1 if they lacked question 2's point originally; scores stay same if they had it.
The 23 students can get at most 23 extra points (none had question 2's point) or at least 0 (all had it). So:
Minimum new total score: 170 + 0 = 170 .
Maximum new total score: 170 + 23 = 193 .
Average = total score ÷ 25 students:
Minimum new average: 170 ÷ 25 = 6.8 .
Maximum new average: 193 ÷ 25 = 7.72 .
The new average ranges from 6.8 to 7.72
it can be < 7 or > 7.
The relationship cannot be determined from the given information.
Answer: D
