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mean median and std dev

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Manager
Joined: 24 Nov 2010
Posts: 215
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Followers: 2

Kudos [?]: 30 [0], given: 7

mean median and std dev [#permalink]  27 Nov 2011, 10:39
00:00

Difficulty:

5% (low)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 1 sessions
A team of researchers measured each of ten subjects' 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
Manager
Joined: 31 May 2011
Posts: 95
Location: India
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 24 [0], given: 4

Re: mean median and std dev [#permalink]  27 Nov 2011, 11:34
dreambeliever wrote:
A team of researchers measured each of ten subjects' 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

IMO E. Mean will not change as the 11th term is itself the mean.
GMAT Instructor
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 232

Kudos [?]: 561 [0], given: 3

Re: mean median and std dev [#permalink]  27 Nov 2011, 13:39
The mean certainly will stay the same if you add a value to a set equal to the set's current mean. Because you are adding a new element which is of a distance of 0 to the mean, the standard deviation will go down (as long as the standard deviation wasn't 0 to begin with) because you will now have more elements clustered close to the mean.

It is impossible to tell what will happen to the median, however, so this is a badly designed question. Where is it from? If you have a set like the following (I'll use four elements instead of ten just for simplicity) :

1, 3, 5, 7

then inserting a new element equal to the mean, which is 4, will not change the median; the median will still be 4. However, if you have this set:

0, 2, 4, 10

then if we insert an element equal to the mean of 4, the median changes from 3 to 4.
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Manager
Joined: 24 Nov 2010
Posts: 215
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Followers: 2

Kudos [?]: 30 [0], given: 7

Re: mean median and std dev [#permalink]  28 Nov 2011, 07:49
yeah i agree that the question's design is not the best because the median may or may not change. this is why i posted it here. Thanks for confirming Ian! It is from Jeff Sackmann's challenge series.
OA was B.
Re: mean median and std dev   [#permalink] 28 Nov 2011, 07:49
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