Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A team of researchers measured each of ten subjects' reactio [#permalink]

Show Tags

27 Nov 2011, 10:39

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

18% (02:08) correct
82% (00:49) wrong based on 38 sessions

HideShow timer Statistics

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

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.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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.

A team of researchers measured each of ten subject's [#permalink]

Show Tags

19 May 2014, 05:08

Hi Guys, could not find the solution to this anywhere on the forum: Please help:

A team of researchers measured each of ten subjectsíreaction 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

The answer as per the hacks solution set is B - but I don't agree because:

1. if you add a term that is equal to the mean of the set, how would it change the SD? since SD is the squared distance from the mean, adding a term that is equal to the mean should not change the SD, right?

2. if you add a term that is equal to the mean of the set, it shouldn't change the mean either right? I tried this by using the mean of 2,3,4 and then 2,3,3,4

3. The median, could change, because with 11 terms, the median should become the 6th term; previously it was the average of the 5th and 6th term?

Please let me know if I am right, or if the hacks answer (B) is correct?

Hi Guys, could not find the solution to this anywhere on the forum: Please help:

A team of researchers measured each of ten subjectsíreaction 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

The answer as per the hacks solution set is B - but I don't agree because:

1. if you add a term that is equal to the mean of the set, how would it change the SD? since SD is the squared distance from the mean, adding a term that is equal to the mean should not change the SD, right?

2. if you add a term that is equal to the mean of the set, it shouldn't change the mean either right? I tried this by using the mean of 2,3,4 and then 2,3,3,4

3. The median, could change, because with 11 terms, the median should become the 6th term; previously it was the average of the 5th and 6th term?

Please let me know if I am right, or if the hacks answer (B) is correct?

Merging similar topics. Please refer to the discussion above.
_________________

Re: A team of researchers measured each of ten subjects' reactio [#permalink]

Show Tags

19 May 2014, 06:06

Quote:

1. if you add a term that is equal to the mean of the set, how would it change the SD? since SD is the squared distance from the mean, adding a term that is equal to the mean should not change the SD, right?

Standard deviation is the squareroot of the sum of squared distance from the mean divided by the number of elements in the set. Because we have 11 data points instead of 10, we divide the sum of squared distances by 11 instead of 10. This changes the standard deviation.

Quote:

2. if you add a term that is equal to the mean of the set, it shouldn't change the mean either right? I tried this by using the mean of 2,3,4 and then 2,3,3,4

Correct, it does not change the mean.

Quote:

3. The median, could change, because with 11 terms, the median should become the 6th term; previously it was the average of the 5th and 6th term?

Correct, the median could change.

This is a poor question as it asks what would change. Either the standard deviation will change, or both the standard deviation and median will change.
_________________

Hi Guys, could not find the solution to this anywhere on the forum: Please help:

A team of researchers measured each of ten subjectsíreaction 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

The answer as per the hacks solution set is B - but I don't agree because:

1. if you add a term that is equal to the mean of the set, how would it change the SD? since SD is the squared distance from the mean, adding a term that is equal to the mean should not change the SD, right?

2. if you add a term that is equal to the mean of the set, it shouldn't change the mean either right? I tried this by using the mean of 2,3,4 and then 2,3,3,4

3. The median, could change, because with 11 terms, the median should become the 6th term; previously it was the average of the 5th and 6th term?

Please let me know if I am right, or if the hacks answer (B) is correct?

As for your questions:

1. The standard deviation will decrease.

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

So, if you add a value to a set equal to the set's current mean, the data will be less widespread, hence the SD will decrease (if the SD wasn't 0 for the initial set).

2. The mean will not change.

3. The median may or may not change.

So, as you see, the question is flawed and you can ignore it.
_________________

Re: A team of researchers measured each of ten subject's [#permalink]

Show Tags

19 May 2014, 06:11

brobeedle wrote:

Hi Guys, could not find the solution to this anywhere on the forum: Please help:

A team of researchers measured each of ten subjectsíreaction 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

The answer as per the hacks solution set is B - but I don't agree because:

1. if you add a term that is equal to the mean of the set, how would it change the SD? since SD is the squared distance from the mean, adding a term that is equal to the mean should not change the SD, right?

2. if you add a term that is equal to the mean of the set, it shouldn't change the mean either right? I tried this by using the mean of 2,3,4 and then 2,3,3,4

3. The median, could change, because with 11 terms, the median should become the 6th term; previously it was the average of the 5th and 6th term?

Please let me know if I am right, or if the hacks answer (B) is correct?

r

If the mean for first 10 terms in a, and the term added is a again, the new mean is (10a + a)/11 =a which means the mean remains same.

In case median is not equal to mean for the initial 10 numbers, the new median will be this number we added. Hence, median will change

The SD will also change as the number of terms increases from 10 to 11. Please note that the sum of squares will remain the same though. SD will therefore decrease.

Thus, the answer is E).

The answer can also be reached by taking 10 values as 1,2,3,4,5,6,7,8,9,12

The mean will be 5.7

Now, if a 11th term equal to mean is added, we get new mean again as 5.5

Median of 1,2,3,4,5,6,7,8,9,12 will be 5.5 but median of 1,2,3,4,5,5.7,6,7,8,9,12 is 5.7 which is different from earlier median

In case of SD we have to find sum of (xi - mean)^2. This sum is same is both cases as 11th term is equal to the mean and will give us 0. But N is 10 in first case, and 11 in second. Thus, SD will also change.

Hi Guys, could not find the solution to this anywhere on the forum: Please help:

A team of researchers measured each of ten subjectsíreaction 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

The answer as per the hacks solution set is B - but I don't agree because:

1. if you add a term that is equal to the mean of the set, how would it change the SD? since SD is the squared distance from the mean, adding a term that is equal to the mean should not change the SD, right?

2. if you add a term that is equal to the mean of the set, it shouldn't change the mean either right? I tried this by using the mean of 2,3,4 and then 2,3,3,4

3. The median, could change, because with 11 terms, the median should become the 6th term; previously it was the average of the 5th and 6th term?

Please let me know if I am right, or if the hacks answer (B) is correct?

r

If the mean for first 10 terms in a, and the term added is a again, the new mean is (10a + a)/11 =a which means the mean remains same.

In case median is not equal to mean for the initial 10 numbers, the new median will be this number we added. Hence, median will change

The SD will also change as the number of terms increases from 10 to 11. Please note that the sum of squares will remain the same though. SD will therefore decrease.

Thus, the answer is E).

The answer can also be reached by taking 10 values as 1,2,3,4,5,6,7,8,9,12

The mean will be 5.7

Now, if a 11th term equal to mean is added, we get new mean again as 5.5

Median of 1,2,3,4,5,6,7,8,9,12 will be 5.5 but median of 1,2,3,4,5,5.7,6,7,8,9,12 is 5.7 which is different from earlier median

In case of SD we have to find sum of (xi - mean)^2. This sum is same is both cases as 11th term is equal to the mean and will give us 0. But N is 10 in first case, and 11 in second. Thus, SD will also change.

I hope it is clear now.

Kudos if you like the response!!!

The median could change but it does not mean that it will change in all cases.

If the set is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then adding a new element equal to the mean, which is 5.5, will not change the median.
_________________

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...