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The average (arithmetic mean) score of Class Qs students is greater t
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03 Oct 2023, 23:25
03 Oct 2023, 23:25
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The average (arithmetic mean) score of Class Q’s students is greater than the average (arithmetic mean) score of Class P’s students. Also, the median score of Class Q’s students is greater than the median score of Class P’s students.
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.
Quantity A |
Quantity B |
Standard deviation of the scores of Class P’s students |
Standard deviation of the scores of Class Q’s students |
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 average (arithmetic mean) score of Class Qs students is greater t
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13 Jan 2024, 06:21
13 Jan 2024, 06:21
Expert Reply
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Re: The average (arithmetic mean) score of Class Qs students is greater t
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17 Jan 2024, 12:00
17 Jan 2024, 12:00
1
First, remember that Standard Deviation (SD) measures how "spread out" the numbers within a set are.
We're given no information on regarding the individual numbers within each set are, which we need to determine SD. (Only info we got was regarding the relationship between the whole sets.) Therefore, D is the right answer.
To demonstrate, let's say that the scores of Class P were: {60, 70, 80}
- The mean and median are both 70
- The SD is 10
And the scores of Class Q were: {70, 80, 90}
- The mean and median are both 80 (which are both greater than Class P's of 70)
- The SD is 10
OR
The scores of Class Q were: {80, 80, 80}
- The mean and median are both 80 (which are both greater than Class P's of 70)
- The SD is 0
We can see that the Standard Deviation can vary between Class P and Q, without affecting median/mean.
We're given no information on regarding the individual numbers within each set are, which we need to determine SD. (Only info we got was regarding the relationship between the whole sets.) Therefore, D is the right answer.
To demonstrate, let's say that the scores of Class P were: {60, 70, 80}
- The mean and median are both 70
- The SD is 10
And the scores of Class Q were: {70, 80, 90}
- The mean and median are both 80 (which are both greater than Class P's of 70)
- The SD is 10
OR
The scores of Class Q were: {80, 80, 80}
- The mean and median are both 80 (which are both greater than Class P's of 70)
- The SD is 0
We can see that the Standard Deviation can vary between Class P and Q, without affecting median/mean.
