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A team of researchers measured each of ten subjects’ reaction time to

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Carcass
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A team of researchers measured each of ten subjects’ reaction time to [#permalink] New post   18 Aug 2021, 05:03
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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


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Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
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Re: A team of researchers measured each of ten subjects’ reaction time to [#permalink] New post   19 Aug 2021, 09:26
and when data is skewed, median should change too
:(

Carcass 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


Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book
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Re: A team of researchers measured each of ten subjects’ reaction time to [#permalink] New post   19 Aug 2021, 21:48
Hi shouldnt the median also change for this sum?
I considered two sets , and it changes in one and doesn't in another
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A team of researchers measured each of ten subjects’ reaction time to [#permalink] New post   19 Aug 2021, 22:16
Hi There!

The median does not always change.
Consider a set A= a,b,c,d,4,6,e,f,g,h
The median here will be 5

Now, if we add 5 in the above set as the 11th element
a,b,c,d,4,5,6,e,f,g,h- the new median is 5 as well.

Whereas if we consider some other set there is a possibility that the median change as well, but not a compulsion as it is for SD.

Thus B

Carcass don't you think the question should say something like must change? Because would is open for wide interpretation and median can also be included in such case.

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Re: A team of researchers measured each of ten subjects’ reaction time to [#permalink] New post   19 Aug 2021, 23:10
Yes , i think the question stem needs to be more precise.
What we know is the sd will surely change irrespective of the data set . The median however depends on the data set , hence there is no sureity :) Thank you!
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Re: A team of researchers measured each of ten subjects’ reaction time to [#permalink] New post   20 Aug 2021, 00:24
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Ks1859 wrote:
Hi There!

The median does not always change.
Consider a set A= a,b,c,d,4,6,e,f,g,h
The median here will be 5

Now, if we add 5 in the above set as the 11th element
a,b,c,d,4,5,6,e,f,g,h- the new median is 5 as well.

Whereas if we consider some other set there is a possibility that the median change as well, but not a compulsion as it is for SD.

Thus B

Carcass don't you think the question should say something like must change? Because would is open for wide interpretation and median can also be included in such case.

Regards
S


No

The median is trickier. If none of the original 10 times were identical, the median must have been the average of 2 of those measurements. it's possible that in the original set of 10, the mean and the median were equal; for instance,
that’s the case if the numbers were consecutive. If they were equal, the median stays the same. If the mean and median were not equal, however, it’s possible that the median does change.
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Re: A team of researchers measured each of ten subjects reaction time to [#permalink] New post   17 Oct 2023, 19:37
Carcass 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



Can someone please explain why would only SD change?

I don't think SD would change, because the 11th data point is equivalent to the mean. I could be wrong, too. Carcass any resources that you might recommend to understand how these stats change with changes in a data set?
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Re: A team of researchers measured each of ten subjects reaction time to [#permalink] New post   17 Oct 2023, 22:53
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Here https://gre.myprepclub.com/forum/gre-me ... tml#p83258 the ONLY notion you need for the GRE about SD

Specifically, memorize the table at the bottom of the guide sir
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