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Three classes took the same psychology test. The class sizes
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08 Jan 2019, 10:05
08 Jan 2019, 10:05
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#GREpracticequestion Three classes took the same psychology test.jpg [ 15.87 KiB | Viewed 5745 times ]
Three classes took the same psychology test. The class sizes and (arithmetic) mean scores are shown.
Quantity A |
Quantity B |
The overall (arithmetic) mean score for the 3 classes |
85 |
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.
Retired Moderator
Joined: 10 Apr 2015
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Re: Three classes took the same psychology test. The class sizes
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09 Jan 2019, 08:58
09 Jan 2019, 08:58
2
Carcass wrote:
Attachment:
#GREpracticequestion Three classes took the same psychology test.jpg
Three classes took the same psychology test. The class sizes and (arithmetic) mean scores are shown.
Quantity A |
Quantity B |
The overall (arithmetic) mean score for the 3 classes |
85 |
One approach is to recognize that 89 is 4 GREATER THAN 85, and 81 is 4 LESS THAN 85.
There are 50 students in the class with the average of 89
There are 30 students in the class with the average of 81
Since there are MORE students in the class with the average of 89, that class has a GREATER effect on the overall average of the 3 classes combined.
In other words, the 89-average class will "push" the overall average closer to 89 than does the 81-average class.
So, the OVERALL average will be greater than 85
We get:
QUANTITY A: some value greater than 85
QUANTITY B: 85
Answer: A
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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Three classes took the same psychology test. The class sizes
[#permalink]
09 Jan 2019, 09:03
09 Jan 2019, 09:03
2
Carcass wrote:
Attachment:
#GREpracticequestion Three classes took the same psychology test.jpg
Three classes took the same psychology test. The class sizes and (arithmetic) mean scores are shown.
Quantity A |
Quantity B |
The overall (arithmetic) mean score for the 3 classes |
85 |
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.
We can also use the weighted average formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
There are 100 students in total.
Class 1 (with an average of 89) comprises 50/100 of all groups combined
Class 2 (with an average of 81) comprises 30/100 of all groups combined
Class 3 (with an average of 85) comprises 20/100 of all groups combined
Apply the formula to get:
Weighted average of groups combined = (50/100)(89) + (30/100)(81) + (20/100)(85)
= (1/2)(89) + (3/10)(81) + (1/5)(85)
= 85.8
We get:
QUANTITY A: 85.8
QUANTITY B: 85
Answer: A
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