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Mean,median,SD

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by tapanmittal » Fri Jun 19, 2015 9:56 pm
A team of researchers measured each of ten subjectsÂ’reaction
time to a certain stimulus and calculated the mean, median, and
standard deviation of the measurements. If none of the reaction
times were identical and an eleventh data point were added that
was equal to the mean of the initial group of ten, which of these
three statistics would change?
(A) The median only
(B) The standard deviation only
(C) The mean and the median
(D) The mean and the standard deviation
(E) The median and the standard deviation

OA is B
As per my understanding,it should be E.
Please explain.
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by theCEO » Fri Jun 19, 2015 10:30 pm
tapanmittal wrote:A team of researchers measured each of ten subjectsÂ’reaction
time to a certain stimulus and calculated the mean, median, and
standard deviation of the measurements. If none of the reaction
times were identical and an eleventh data point were added that
was equal to the mean of the initial group of ten, which of these
three statistics would change?
(A) The median only
(B) The standard deviation only
(C) The mean and the median
(D) The mean and the standard deviation
(E) The median and the standard deviation

OA is B
As per my understanding,it should be E.
Please explain.
This question seems flawed. What is the source? Depending on the numbers, E could be the answer as well as B.
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by Ian Stewart » Fri Jun 19, 2015 10:43 pm
tapanmittal wrote: As per my understanding,it should be E.
Your understanding is correct, I think, but it's not clear what the question is asking - is it asking whether the median could change, or whether it must change? Those are very different questions.

We know the standard deviation must drop, and the mean must stay the same. The median might stay the same, or might change. We can see that by looking at sets with 4 elements for simplicity - the same will be true when you have 10 elements. If your set is symmetric (equally spaced, say), then the median will definitely not change:

0, 2, 4, 6 ---> mean and median are both 3

0, 2, 3, 4, 6 --> median is still 3

but if you invent any random set which is not symmetric, the median will almost always change:

0, 2, 4, 30 --> mean is 9, and median is 3

0, 2, 4, 9, 30 --> median goes up to 4

So the median might change, or might not. I don't know if that makes the answer B or E, because I can't guess what the question means when it says "which statistics would change". Where is the question from?
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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by tapanmittal » Fri Jun 19, 2015 10:43 pm
Source-->Jeff Sackmann. To be more clear,it should be mentioned whether the numbers are in some sequence or not.
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by Matt@VeritasPrep » Tue Jun 23, 2015 6:11 pm
Definitely a sloppy prompt, but I think we have to interpret "would" as "must", no?

The GMAT itself *would* (there's that word again :D) be clearer though.
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