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set containng only one element

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Director
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set containng only one element [#permalink] New post 09 Oct 2009, 00:19
Hey guys I get a little confused when I am faced with a set containng only one element so thought will meke it clear once and for all:

{-5}
Mean:-5
Median: ??? (explanations?)
Mode:-5 or none
Range:0
Standard Deviation:0

Set with identical values:
Range=0,S.D=0
Inputs??
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Re: set containng only one element [#permalink] New post 10 Oct 2009, 11:03
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tejal777 wrote:
Hey guys I get a little confused when I am faced with a set containng only one element so thought will meke it clear once and for all:

{-5}
Mean:-5
Median: ??? (explanations?)
Mode:-5 or none
Range:0
Standard Deviation:0

Set with identical values:
Range=0,S.D=0
Inputs??


I don't think I've ever seen a one-element set in a GMAT question, but the median of the set {-5} is -5, because that's the 'middle number' -- it's the only number, so it must be in the middle. If each element in a set occurs with equal frequency, the set has no mode, so this set has no mode, though that's a technicality that you will never need to worry about in a GMAT question.

If a set has more than one element, and all values are equal to some number x, then the range and s.d. are both zero, and the mean, median and mode are all equal to x.
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Re: set containng only one element [#permalink] New post 19 Feb 2013, 07:39
Bunuel,

Is mode tested on GMAT?

Also, why is the range 'zero' for a 1 element set?
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Re: set containng only one element [#permalink] New post 19 Feb 2013, 09:24
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The range is 0 because the largest and smallest elements are equal, and range = largest - smallest.

I've never seen even one real GMAT question which tested the mode, and I've seen several thousand real GMAT questions. I did read a test taker debrief once however that mentioned the mode appearing in a question, so while it's extremely unlikely that you will see it, I'd suggest you at least know what the mode is. There's nothing more you need to know besides the definition.
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Re: set containng only one element   [#permalink] 19 Feb 2013, 09:24
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set containng only one element

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