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The 75th percentile on a test corresponded to a score of 700
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28 Jul 2018, 16:26
28 Jul 2018, 16:26
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The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.
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 |
A 95th percentile score |
\(800\) |
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.
Re: The 75th percentile on a test corresponded to a score of 700
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12 Aug 2018, 16:18
12 Aug 2018, 16:18
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Explanation
Scoring scales on a test are not necessarily linear, so do not line up the difference in percentiles with the difference in score; it is not possible to make any predictions about other percentiles.
For all you know, 750 could be the 95th percentile score—or 963 could be. All that is certain is that 25% of the scores are ≤ 450, while 50% of the scores are > 450 and ≤ 700, and 25% of the scores are > 700.
Scoring scales on a test are not necessarily linear, so do not line up the difference in percentiles with the difference in score; it is not possible to make any predictions about other percentiles.
For all you know, 750 could be the 95th percentile score—or 963 could be. All that is certain is that 25% of the scores are ≤ 450, while 50% of the scores are > 450 and ≤ 700, and 25% of the scores are > 700.
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Re: The 75th percentile on a test corresponded to a score of 700
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11 Aug 2019, 09:43
11 Aug 2019, 09:43
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sandy wrote:
The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.
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 |
A 95th percentile score |
\(800\) |
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.
IMPORTANT: Many students will assume that the above distribution of scores is a NORMAL distribution.
However, since this is not mentioned, we can't assume that we have a normal distribution.
This means the scores don't follow any particular pattern (as in a normal distribution)
To begin, let's say there are 100 scores in TOTAL.
NOTE:
If a score of 450 is in the 25th percentile, then 25 scores are less than 450, and...
If a score of 700 is in the 75th percentile, then 75 scores are less than 700
So, it COULD be the case that, when arranged in ASCENDING order, the first 76 value are as follows:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700.....}
The 76 values above satisfy the given information.
The remaining 24 scores can be pretty much anything (as long as they're greater than 700)
So, it COULD be the case that the next 19 values are 701
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, .....}
At this point, we've listed 95 of the 100 values.
So, the next value in the list will be the 95th percentile score.
Consider these two possible cases:
case i: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 702.....}
In this case, 702 is the 95th percentile score.
Since 702 < 800, Quantity B is greater
case ii: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 1,000,000.....}
In this case, 1,000,000 is the 95th percentile score.
Since 1,000,000 > 800, Quantity A is greater
Answer: D
Cheers,
Brent
