X series : 200, 400, 600..... 1200
Does series Y have more S.D than series X?
a) Average of Y = 500
b) Range of Y >= 2000
with explanation please.
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X or Y series
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tohellandback
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IMO B,
1) we need to know how far the numbers in the series are from the mean.
INSUFF
2)lets take the case when the SD can be minimum
{0,2000}- mean 1000
SD =sqrt(2*(1000)^2)/2
SD of series X= sqrt(2*((100)^2+(300)^2+(500)^2))/6
SD of Y > SD of X
SUFF
1) we need to know how far the numbers in the series are from the mean.
INSUFF
2)lets take the case when the SD can be minimum
{0,2000}- mean 1000
SD =sqrt(2*(1000)^2)/2
SD of series X= sqrt(2*((100)^2+(300)^2+(500)^2))/6
SD of Y > SD of X
SUFF
The powers of two are bloody impolite!!
IMO E)
since we don't know how many numbers series Y contains,
the SD can be anything
if series Y contain (0,2000, infinite numbers of 500)
the mean will be infinitely close to 500, while SD will be infinitely close to zero.
and it can be the other way if Y contains (0,0,0,2000) the mean will be 500, while SD is definitely greater than that of series X.
what's OA?
since we don't know how many numbers series Y contains,
the SD can be anything
if series Y contain (0,2000, infinite numbers of 500)
the mean will be infinitely close to 500, while SD will be infinitely close to zero.
and it can be the other way if Y contains (0,0,0,2000) the mean will be 500, while SD is definitely greater than that of series X.
what's OA?
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Ian Stewart
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This is a suspect question, because it uses the word 'series', but goes on to list sets or sequences of numbers. The word 'series' has a precise definition in mathematics - one you don't need to know for the GMAT - and the question is nonsensical if one interprets it literally; a series doesn't have a standard deviation at all.
If you replace the word 'series' with 'set', zenithexe's explanation is perfect. Standard deviation is based on the distances between things in the set, while the mean is based on the sizes of things in the set, so Statement 1 is completely irrelevant. Range only takes into account two values - the extremes - while standard deviation takes into account all values, so Statement 2 isn't very useful. For example, you could have the set:
{-500, 500,500,500,500,500,500,500...,500,1500}
with a trillion 500s in the middle. This set has a mean of 500, a range of 2000, and a standard deviation almost equal to zero. Of course, that's essentially what zenithexe said above.
In any case, it's a dodgy question, and if you don't even have the OA, I'm not sure why you're using the source.
If you replace the word 'series' with 'set', zenithexe's explanation is perfect. Standard deviation is based on the distances between things in the set, while the mean is based on the sizes of things in the set, so Statement 1 is completely irrelevant. Range only takes into account two values - the extremes - while standard deviation takes into account all values, so Statement 2 isn't very useful. For example, you could have the set:
{-500, 500,500,500,500,500,500,500...,500,1500}
with a trillion 500s in the middle. This set has a mean of 500, a range of 2000, and a standard deviation almost equal to zero. Of course, that's essentially what zenithexe said above.
In any case, it's a dodgy question, and if you don't even have the OA, I'm not sure why you're using the source.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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