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 greatercase 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 greaterAnswer: D
Cheers,
Brent