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27 Nov 2011, 11:39
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B
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Difficulty:
95%
(hard)
Question Stats:
18% (02:07) correct
82%
(01:27)
wrong
based on 22
sessions
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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
(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
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27 Nov 2011, 14:39
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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.
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.
28 Nov 2011, 08:49
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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.
OA was B.
