Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 Apr 2016, 13:32

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# PS questions about standard deviation.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 32531
Followers: 5624

Kudos [?]: 68230 [0], given: 9797

### Show Tags

30 Oct 2009, 14:11
Expert's post
GMAT TIGER wrote:
Bunuel wrote:
Questions #1 and #9 are solved incorrectly. One of two answers for #6 is incorrect.

Are you talking seriously???

Yes. Your second solution for question #9 is correct. Indeed there are 6 possibilities and 2 pairs have the same SD, so there would be 4 different SD.

As for #1: if it would be E {0,8}, wouldn't these two numbers stretch the set making SD bigger? As {0,8} are too far from the the mean.

And for #6: 2 answers were given (by others) to this question and one of them is incorrect.

So yes, I'm serious. But maybe I didn't get your question right...
_________________
SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 64

Kudos [?]: 649 [0], given: 19

### Show Tags

30 Oct 2009, 17:23
Bunuel wrote:
GMAT TIGER wrote:
Bunuel wrote:
Questions #1 and #9 are solved incorrectly. One of two answers for #6 is incorrect.

Are you talking seriously???

Yes. Your second solution for question #9 is correct. Indeed there are 6 possibilities and 2 pairs have the same SD, so there would be 4 different SD.

As for #1: if it would be E {0,8}, wouldn't these two numbers stretch the set making SD bigger? As {0,8} are too far from the the mean.

Agree with your logic but did you check whether other choices could deviate more further than E?
So what is your OA and workout for #1.
Did you solve it or just guessing? If you solve it, you will find E as the closest.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 32531
Followers: 5624

Kudos [?]: 68230 [0], given: 9797

### Show Tags

30 Oct 2009, 17:44
Expert's post
GMAT TIGER wrote:
Agree with your logic but did you check whether other choices could deviate more further than E?
So what is your OA and workout for #1.
Did you solve it or just guessing? If you solve it, you will find E as the closest.

Frankly speaking when I solved this for the first time I didn't calculated SD-s. Just trusted my logic, then compared my answer to the OA and as they matched I didn't double checked my own solution and OA.

But know I did it. And I can say it again E {0,8} is not correct.

Maybe there is some misunderstanding in stem?
_________________
Senior Manager
Joined: 18 Aug 2009
Posts: 303
Followers: 3

Kudos [?]: 200 [0], given: 9

### Show Tags

30 Oct 2009, 19:05
1
This post was
BOOKMARKED
GMAT TIGER wrote:
gmattokyo wrote:
9. E is a collection of four odd integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
-----------------------------------

(C) 5
Not very sure of this one... would wait for an expert solution.
Given that the range is 4. So pick up any set of odd numbers (SD will be same for the scenarios, all the set of 4 odd integers with range of 4 will have 3 unique members).
Possible sets (each with a different SD):
1. [1,5,1,1]
2. [1,5,5,5]
3. [1,5,3,3]
4. [1,5,1,3]
5. [1,5,1,5]
6. [1,5,3,5]

total of 6. 1st and 2nd have the same SD. Left with 5 other cases.

1. [1,5,1,1] and 2. [1,5,5,5] have SD of 2.
3. [1,5,3,3] has a SD of 1.63.
4. [1,5,1,3] and 6. [1,5,3,5] have 1.91.
5. [1,5,1,5] has a SD of 2.31.

So there are altogather 4 different SDs.

Thanks to GMAT TIGER for the correction and to Bunuel for giving us kool practice.
SVP
Joined: 29 Aug 2007
Posts: 2492
Followers: 64

Kudos [?]: 649 [0], given: 19

### Show Tags

30 Oct 2009, 20:10
Bunuel wrote:
GMAT TIGER wrote:
Agree with your logic but did you check whether other choices could deviate more further than E?
So what is your OA and workout for #1.
Did you solve it or just guessing? If you solve it, you will find E as the closest.

Frankly speaking when I solved this for the first time I didn't calculated SD-s. Just trusted my logic, then compared my answer to the OA and as they matched I didn't double checked my own solution and OA.

But know I did it. And I can say it again E {0,8} is not correct.

Maybe there is some misunderstanding in stem?

lol.

Probably the difference is from how the SDs are calculated. I used (n-1) instead of n while dividing the sum of the sqare dev. If n is used, then it is (2, 6).
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 32531
Followers: 5624

Kudos [?]: 68230 [5] , given: 9797

### Show Tags

04 Nov 2009, 17:45
5
KUDOS
Expert's post
5
This post was
BOOKMARKED

1. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8

2. A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the following pairs of data, when added to the list must result in a list of 102 data with the standard deviation less than d?
(A) 0 and 6
(B) 0 and 12
(C) 0 and 0
(D) -6 and 0
(E) 6 and 6

3. For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82

4. Which of the following distribution of numbers has the greatest standard deviation?
(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}

5. Which of the following has the same standard deviation as {s,r,t}?
I. {r-2, s-2, t-2}
II. {0, s-t, s-r}
III. {|r|, |s|, |t|}
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

6. A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than m+d?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%

7. Which of the following data sets has the third largest standard deviation?
(A) {1, 2, 3, 4, 5}
(B) {2, 3, 3, 3, 4}
(C) {2, 2, 2, 4, 5}
(D) {0, 2, 3, 4, 6}
(E) {-1, 1, 3, 5, 7}

8. The table below represents three sets of numbers with their respective medians, means and standard deviations. The third set, Set [A+B], denotes the set that is formed by combining Set A and Set B.

Median Mean StandardDeviation
Set A: X, Y, Z.
Set B: L, M, N.
Set [A + B]: Q, R, S.
If X – Y > 0 and L – M = 0, then which of the following must be true?
I. Z > N
II. R > M
III. Q > R
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) None

9. E is a collection of four odd integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

11. Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
(A) 10.5
(B) 11
(C) 11.5
(D) 12
(E) 12.5

_________________
Intern
Joined: 17 Nov 2009
Posts: 37
Schools: University of Toronto, Mcgill, Queens
Followers: 0

Kudos [?]: 75 [1] , given: 9

### Show Tags

18 Dec 2009, 05:05
1
KUDOS
GMAT TIGER wrote:
Bunuel wrote:
1. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8

E. I got 0 and 8.

I don't think Answer will be E, here i'll prove it and you can also check with the calculations that E cannot be true.

With the given set the mean = 4 (as it is set of consecutive even integers therefore, 8+0/2 = 4 )

For all the options the mean remains 4 (as they add 8 to the total it will be divided by 7)

As the values are close to the mean then SD will be lower than the original SD and if the values are far from the mean than SD will be higher.

so D is the option which is not closer and not far from the mean.
_________________

--Action is the foundational key to all success.

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1181
Followers: 366

Kudos [?]: 1203 [3] , given: 4

### Show Tags

18 Dec 2009, 09:07
3
KUDOS
Expert's post
Bunuel wrote:

8. The table below represents three sets of numbers with their respective medians, means and standard deviations. The third set, Set [A+B], denotes the set that is formed by combining Set A and Set B.

Median Mean StandardDeviation
Set A: X, Y, Z.
Set B: L, M, N.
Set [A + B]: Q, R, S.
If X – Y > 0 and L – M = 0, then which of the following must be true?
I. Z > N
II. R > M
III. Q > R
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) None

We have no information that might allow us to compare Z and N, so I need not be true. For II, without knowing the relationship between Y and M, we cannot decide whether R is larger than M. For III, if set A is {0, 3, 4}, then the median of A is larger than the mean. If set B is {13}, then the median of B is equal to the mean. So these sets agree with the conditions given. Combining the sets, we have {0, 3, 4, 13}, which has a median of 3.5 and a mean of 5; the median is not greater than the mean. So III need not be true and the answer is E.
_________________

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

Intern
Joined: 25 Jul 2009
Posts: 32
Location: Lahore, Pakistan
Schools: going to Melbourne Business School
Followers: 2

Kudos [?]: 8 [0], given: 0

### Show Tags

02 Jan 2010, 11:57
Bunuel wrote:
GMAT TIGER wrote:
Agree with your logic but did you check whether other choices could deviate more further than E?
So what is your OA and workout for #1.
Did you solve it or just guessing? If you solve it, you will find E as the closest.

Frankly speaking when I solved this for the first time I didn't calculated SD-s. Just trusted my logic, then compared my answer to the OA and as they matched I didn't double checked my own solution and OA.

But know I did it. And I can say it again E {0,8} is not correct.

Maybe there is some misunderstanding in stem?

Last edited by hamza on 02 Jan 2010, 13:06, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 32531
Followers: 5624

Kudos [?]: 68230 [0], given: 9797

### Show Tags

02 Jan 2010, 12:02
Expert's post
hamza wrote:
Bunuel wrote:
GMAT TIGER wrote:
Agree with your logic but did you check whether other choices could deviate more further than E?
So what is your OA and workout for #1.
Did you solve it or just guessing? If you solve it, you will find E as the closest.

Frankly speaking when I solved this for the first time I didn't calculated SD-s. Just trusted my logic, then compared my answer to the OA and as they matched I didn't double checked my own solution and OA.

But know I did it. And I can say it again E {0,8} is not correct.

Maybe there is some misunderstanding in stem?

Answer E for Q1 is not correct, OA is D. Pleas refer to my post with OA-s.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 32531
Followers: 5624

Kudos [?]: 68230 [4] , given: 9797

### Show Tags

02 Jan 2010, 13:37
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
hamza wrote:

1. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8

I guess this is not real GMAT question as to answer this question with 100% certainty you should calculate SD for two sets and GMAT usually do not require actual calculation of SD. Though it's possible to eliminate 3 wrong answers at the beginning.

Mean is 4 and so are the means of all 5 pairs from answers choices.

A. (-1, 9) These two numbers are farthest from the mean and they will stretch the set making SD bigger

B. (4, 4) These two numbers are closest to the mean and the will shrink the set making SD smaller

C. (3, 5) Suitable option so far

D. (2, 6) Suitable option so far

E. (0, 8) These two numbers are also far from mean and they will also stretch the set making SD bigger.

So, when I looked at the options C and D I assumed that C is also too close to the mean and it will affect it more than D. So I ended with D and was correct. But still my logic eliminating C was not sure thing, without the calculations.
_________________
Intern
Joined: 25 Jul 2009
Posts: 32
Location: Lahore, Pakistan
Schools: going to Melbourne Business School
Followers: 2

Kudos [?]: 8 [0], given: 0

### Show Tags

02 Jan 2010, 23:23
Thanks a lot Bunuel for all the SD questions, I think SD, by means is covered,

Thanks again...
Intern
Joined: 07 Apr 2010
Posts: 23
Followers: 1

Kudos [?]: 9 [6] , given: 30

### Show Tags

15 May 2010, 21:18
6
KUDOS
1
This post was
BOOKMARKED
Convincing explanation for question 1.
Bunuel wrote:
1. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8

Mean = 4
Var = (16+4+0+4+16)/5 = $$40/5 = 8$$
After addition of 2 numbers, New Var = $$(40+x)/7$$
The question is What x will pitch New Var closest to 8 so that 56/7 = 8
OR Which of the options will give a value of x that is closest to 16
So from the 5 options find out which (deviation^2) from 4 is closest to 16
Naked eye will tell you that (A), (B) are a long shot.
(C) 1^2 + 1^2 = 2
(D) 2^2 + 2^2 = 8 ==> |16-8| = 8
(E) 4^2 + 4^2 = 32 ==> |16-32| = 16
So option (D) gives an SD that is closest to the original SD.
_________________

In a Normal Distribution, only the Average 'Stand Out'

Manager
Joined: 04 Apr 2009
Posts: 68
Location: United Kingdom
Schools: Cornell
Followers: 1

Kudos [?]: 29 [1] , given: 6

### Show Tags

06 Jun 2010, 12:39
1
KUDOS
Really good collection of questions....I think SD is more or less covered now
Director
Joined: 25 Aug 2007
Posts: 954
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Followers: 70

Kudos [?]: 1056 [0], given: 40

### Show Tags

08 Jun 2010, 07:17
Bunuel,

I think the statement in the Q10 is incorrect. Some typo error, IMO:

10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations AWAY from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

Bunuel wrote:
10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

_________________

Tricky Quant problems: 50-tricky-questions-92834.html
Important Grammer Fundamentals: key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Math Expert
Joined: 02 Sep 2009
Posts: 32531
Followers: 5624

Kudos [?]: 68230 [1] , given: 9797

### Show Tags

08 Jun 2010, 08:13
1
KUDOS
Expert's post
ykaiim wrote:
Bunuel,

I think the statement in the Q10 is incorrect. Some typo error, IMO:

10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations AWAY from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

Bunuel wrote:
10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?

(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

No typo there: the question is from GmatPrep but basically it's the same as you wrote.
_________________
Director
Joined: 25 Aug 2007
Posts: 954
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Followers: 70

Kudos [?]: 1056 [0], given: 40

### Show Tags

08 Jun 2010, 08:22
I found the Q11 in GMATPrep and based on the explaination for it, I asked you.

As per the question:
10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations AWAY from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

So, the answer would be > 20+2.5x3 or >27.5, while none of the options say this.
But, if we are given that the required value is 2.5 SD more away then we can find the new value = 12.
_________________

Tricky Quant problems: 50-tricky-questions-92834.html
Important Grammer Fundamentals: key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Math Expert
Joined: 02 Sep 2009
Posts: 32531
Followers: 5624

Kudos [?]: 68230 [2] , given: 9797

### Show Tags

08 Jun 2010, 08:48
2
KUDOS
Expert's post
ykaiim wrote:
I found the Q11 in GMATPrep and based on the explaination for it, I asked you.

As per the question:
10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations AWAY from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

So, the answer would be > 20+2.5x3 or >27.5, while none of the options say this.
But, if we are given that the required value is 2.5 SD more away then we can find the new value = 12.

I don't quite understand your question... Again the question is from GmarPrep and there is no word "away" in it (at least in the version I have).

Value is more than 2.5SD from the mean means that the distance between the mean and the value must be more than 2.5SD=7.5. So the value either < 12.5 or > 27.5.

_________________
Manager
Joined: 27 May 2010
Posts: 102
Followers: 2

Kudos [?]: 6 [0], given: 13

### Show Tags

16 Aug 2010, 08:12
good practice material.
Intern
Joined: 22 May 2010
Posts: 32
Followers: 0

Kudos [?]: 7 [0], given: 85

### Show Tags

31 Oct 2010, 16:50
Bunuel,
First of all thanks for all the wonderful material that you compile and post here on this forum. I have been following lot of your math related posts for past few days. Your posts are great help in the gmat prep.

I was wondering if you have solutions for these PS SD questions? - specially to Q#8 & 9?

Bunuel wrote:

1. A set of data consists of the following 5 numbers: 0,2,4,6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8

2. A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the following pairs of data, when added to the list must result in a list of 102 data with the standard deviation less than d?
(A) 0 and 6
(B) 0 and 12
(C) 0 and 0
(D) -6 and 0
(E) 6 and 6

3. For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82

4. Which of the following distribution of numbers has the greatest standard deviation?
(A) {-3, 1, 2}
(B) {-2, -1, 1, 2}
(C) {3, 5, 7}
(D) {-1, 2, 3, 4}
(E) {0, 2, 4}

5. Which of the following has the same standard deviation as {s,r,t}?
I. {r-2, s-2, t-2}
II. {0, s-t, s-r}
III. {|r|, |s|, |t|}
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

6. A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than m+d?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%

7. Which of the following data sets has the third largest standard deviation?
(A) {1, 2, 3, 4, 5}
(B) {2, 3, 3, 3, 4}
(C) {2, 2, 2, 4, 5}
(D) {0, 2, 3, 4, 6}
(E) {-1, 1, 3, 5, 7}

8. The table below represents three sets of numbers with their respective medians, means and standard deviations. The third set, Set [A+B], denotes the set that is formed by combining Set A and Set B.

Median Mean StandardDeviation
Set A: X, Y, Z.
Set B: L, M, N.
Set [A + B]: Q, R, S.
If X – Y > 0 and L – M = 0, then which of the following must be true?
I. Z > N
II. R > M
III. Q > R
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) None

9. E is a collection of four odd integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

10. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5

11. Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
(A) 10.5
(B) 11
(C) 11.5
(D) 12
(E) 12.5

Go to page   Previous    1   2   3   4   5   6    Next  [ 101 posts ]

Similar topics Replies Last post
Similar
Topics:
Hardest Standard Deviation Question Ever 1 13 Oct 2011, 03:03
Standard Deviation question 7 07 Aug 2011, 14:04
Standard deviation 1 03 Aug 2010, 20:05
standard deviation 6 14 Feb 2010, 17:26
Standard Deviation - GMATprep 2 question 6 03 Aug 2009, 04:14
Display posts from previous: Sort by