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The 75th percentile on a test corresponded to a score of 700

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The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 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.

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.
[Reveal] Spoiler: OA

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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 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.
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 11 Aug 2019, 06:37
"750 could be the 95th percentile score—or 963 could be"

How did you get these limits ? Can you please elaborate?
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 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.

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
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 11 Aug 2019, 10:26
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You should deserve more than a kudo Sir., for the amazing , spot-on explanations.

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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 16 Aug 2019, 06:40
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GreenlightTestPrep wrote:
sandy wrote:
The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.

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




Thanks for your explanation.
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 02 Jun 2020, 23:25
GreenlightTestPrep wrote:
sandy wrote:
The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.

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


This was an amazing explanation. I have a small request, just to make my concept clear.

If I attempt this question assuming the scores have a normal distribution, then this is my thought process,

450 is 25%
700 is 75%

700-450 = 250

As they both are equally around the mean, 50% to 75% = 125



700+125 = 825 is ideally what 100% should be ( for linearly distributed graph)

But since this is a normal distribution,

area covered between 50%-75% > area covered between 75-95%

To make them equal, I will have to shift the 95% to the right, which is > 825

It cannot be determined how much > 825 it is supposed to be, hence answer is still D if the above question is modified to a normal distribution.

Please correct me if my thought process is wrong. Thank you.
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 03 Jun 2020, 04:17
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It is indeed correct
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink] New post 03 Jun 2020, 04:55
Carcass wrote:
It is indeed correct


Alright! Thank you
Re: The 75th percentile on a test corresponded to a score of 700   [#permalink] 03 Jun 2020, 04:55
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