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# PS questions about standard deviation.

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Manager
Joined: 05 Nov 2012
Posts: 55
Re: PS questions about standard deviation. [#permalink]

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16 Dec 2015, 23:07
Bunuel wrote:
Questions 1 and 9 are solved incorrectly. One of two answers for 6 is incorrect. 10 and 11 aren't solved yet, though they are relatively easy.

The hardest questions in this set are 8 and 9. Probably they are 750+ problems, so would be interesting to see the solutions for them. Also please note that I don't have the OA for 8!, only my own solution.

Good luck.

Hi Bunuel,

I looked at the solution for question 8 and 9 and couldn't really understand them. Can you help me with a simpler way of doing these 2 questions in the list.

In question 9, I specifically do not get the part: The standard deviation of E must be one of how many numbers?

In question 8, I would request a reattempt to help me explain it.

Thanks again.
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Re: PS questions about standard deviation. [#permalink]

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25 Jul 2016, 19:37
Bunuel wrote:
Questions 1 and 9 are solved incorrectly. One of two answers for 6 is incorrect. 10 and 11 aren't solved yet, though they are relatively easy.

The hardest questions in this set are 8 and 9. Probably they are 750+ problems, so would be interesting to see the solutions for them. Also please note that I don't have the OA for 8!, only my own solution.

Good luck.

Hello Bunuel,

Request you to please post your answers to these questions.
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Posts: 43828
Re: PS questions about standard deviation. [#permalink]

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25 Jul 2016, 20:53
royrijit1 wrote:
Bunuel wrote:
Questions 1 and 9 are solved incorrectly. One of two answers for 6 is incorrect. 10 and 11 aren't solved yet, though they are relatively easy.

The hardest questions in this set are 8 and 9. Probably they are 750+ problems, so would be interesting to see the solutions for them. Also please note that I don't have the OA for 8!, only my own solution.

Good luck.

Hello Bunuel,

Request you to please post your answers to these questions.

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Re: PS questions about standard deviation. [#permalink]

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11 Aug 2016, 17:51
Hi!
Bunuel Sir,
Can I look forward the explanation by you for all those 11 question like you have been solving other special questions in threads please?
Kindly share your solution as they are always an eye opener for me.
Thanks
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Re: PS questions about standard deviation. [#permalink]

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02 Oct 2016, 02:52
1. B
2. E
3. A
4. A
5. D
6. D
7. A
8. A
9. D
10.A
11. A
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Re: PS questions about standard deviation. [#permalink]

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02 Oct 2016, 02:54
1. B
2. E
3. A
4. A
5. D
6. D
7. A
8. A
9. D
10.A
11. A
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Re: PS questions about standard deviation. [#permalink]

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12 Nov 2016, 04:57
GMAT TIGER wrote:
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

Probably C only. III.

Can anyone post a detailed repy for this.

the official answer is E
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Re: PS questions about standard deviation. [#permalink]

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12 Nov 2016, 05:02
AmritaSarkar89 wrote:
GMAT TIGER wrote:
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

Probably C only. III.

Can anyone post a detailed repy for this.

the official answer is E

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Re: PS questions about standard deviation. [#permalink]

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24 Jan 2017, 00:43
1
This post was
BOOKMARKED
IanStewart wrote:
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.

Official answer from Manhattan Prep.

If X – Y > 0, then X > Y and the median of A is greater than the mean of set A. If L – M = 0, then L = M and the median of set B is equal to the mean of set B.

I. NOT NECESSARILY: According to the table, Z > N means that the standard deviation of set A is greater than that of set B. Standard deviation is a measure of how close the terms of a given set are to the mean of the set. If a set has a high standard deviation, its terms are relatively far from the mean. If a set has a low standard deviation, its terms are relatively close to the mean.

Recall that a median separates the set into two as far as the number of terms. There is an equal number of terms both above and below the median. If the median of a set is greater than the mean, however, the terms below the median must collectively be farther from the median than the terms above the median. For example, in the set {1, 89, 90}, the median is 89 and the mean is 60. The median is much greater than the mean because 1 is much farther from 89 than 90 is.

Knowing that the median of set A is greater than the mean of set A just tells us that the terms below set A’s median are further from the median than the terms above set A’s median. This does not necessarily imply that the terms, overall, are further away from the mean than in set B, where the terms below the median are the same distance from the median as the terms above it. In fact, a set in which the mean and median are equal can have a very high standard deviation if the terms are both far below the mean and far above it.

II. NOT NECESSARILY: According to the table, R > M implies that the mean of set [A + B] is greater than the mean of set B. This is not necessarily true. When two sets are combined to form a composite set, the mean of the composite set must either be between the means of the individual sets or be equal to the mean of both of the individual sets. To prove this, consider the simple example of one member sets: A = [3], B = [5], A + B = [3, 5]. In this case the mean of A + B is greater than the mean of A and less than the mean of B. We could easily have reversed this result by reversing the members of sets A and B.

III. NOT NECESSARILY: According to the table, Q > R implies that the median of the set [A + B] is greater than the mean of set [A + B]. We can extend the rule given in statement II to medians as well: when two sets are combined to form a composite set, the median of the composite set must either be between the medians of the individual sets or be equal to the median of one or both of the individual sets. While the median of set A is greater than the mean of set A and the median of set B is equal to the mean of set B, set [A + B] might have a median that is greater or less than the mean of set [A + B].

Therefore none of the statements are necessarily true and the correct answer is E.
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Re: PS questions about standard deviation. [#permalink]

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08 Feb 2017, 11:56
GMAT TIGER wrote:
Bunuel wrote:
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}

Look for range and # of elements in the set.

A set with higher the range and fewer the number of element has the higher SD. i.e. A.

Yes that logic is correct , when we have big out-liner's. But here if we take option A & D .

A have the range of 3, while D has range of 2 (but 1 value greater by 2 , 1 greater by 1 and 1 smaller by 2 again ) so this would appox give the same SD as A ???
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Re: PS questions about standard deviation. [#permalink]

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04 Jun 2017, 07:40
Bunuel: Can we get answers of these questions please?
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04 Jun 2017, 22:27
nupur297 wrote:
Bunuel: Can we get answers of these questions please?

Please go through the discussion. You'll find OAs there as well as may other useful staff.

P.S. OA's are in the following post: https://gmatclub.com/forum/ps-questions ... ml#p647412 Hope it helps.
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29 Jul 2017, 03:29
Hi Bunuel

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}

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}

In the questions such as the above, can we look at the range in each option and mark that option which has the highest range? (I know question #7 says third highest S.D)
But I do understand that if the range is for 2 options in the same is same then we need to calculate SD

Please share your thoughts on the above

Note: - I read through all the comments in the thread but couldn't an expert reply on this
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Re: PS questions about standard deviation. [#permalink]

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31 Jul 2017, 04:20
GMAT TIGER wrote:
Bunuel 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

Thats a real good question however I took more than 5 minuets to understand as I went in a wrong direction.

Since the greatest difference between any two elements in E is 4, different elements in E, lets say, could be: (3, x, x, 7) where x could be any of 3 or 5 or 7.

How many possibilities: {3,3,3,7}, {3,3,5,7}, {3,3,7,7}, {3,5,5,7}, {3,5,7,7}, {3,7,7,7}. So 6.

D.

Can you please explain this in detail
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Re: PS questions about standard deviation. [#permalink]

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31 Jul 2017, 04:33
Hi bunuel can you please explain qn 8 and 9.
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Re: PS questions about standard deviation. [#permalink]

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31 Jul 2017, 04:50
Just for confirmation

When we multiply elements in a list by K, then SD and Mean gets multiplied right.
When we add/subtract by a constant then only mean gets added or subtracted by that constant

mean and median are same when :
1. They are consecutive numbers
2. Evenly spaced numbers
3. Symmetric, ie. Mirror images

ARe there any more to the List

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Re: PS questions about standard deviation. [#permalink]

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15 Aug 2017, 07:20
Icerockboom wrote:
Bunuel wrote:
hamza wrote:

BUNUEL: Please share your logic for Q#1.

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.

We do not need to calculate the deviation, as when we add a new number to a set, it will affect the original SD of the set, in the following way:
[y is the new number added, xav is the arithmatic mean]
|y-xav| < SD -> Decrease SD
|y-xav| > SD -> Increase SD
|y - xav| = SD -> SD remains constant.
So, the nearer the |y-xav| to SD is, the less the SD changes.

Make some comparation, we got the result is D

Well the last rule can't be true. Otherwise answer choice b (4,4) would keep the SD constant. But adding 4 and 4 decreases the SD. Bunuel, can you clarify? Do the other rules hold true?
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Re: PS questions about standard deviation. [#permalink]

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29 Aug 2017, 01:00
GMAT TIGER wrote:
Bunuel wrote:
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}

The order is:
1. (E) {-1, 1, 3, 5, 7}
2. (D) {0, 2, 3, 4, 6}
3. (A) {1, 2, 3, 4, 5}
4. (C) {2, 2, 2, 4, 5}
5. (B) {2, 3, 3, 3, 4}

i.e. A.

The order is:
1. (E) {-1, 1, 3, 5, 7} SD = 4
2. (D) {0, 2, 3, 4, 6} SD= 3
3. (A) {1, 2, 3, 4, 5} SD= 2
4. (C) {2, 2, 2, 4, 5} SD= 3
5. (B) {2, 3, 3, 3, 4} SD= 1

How can A be the answer? SD of ( C ) is greater than SD oF ( D )
The answer should be between D and C
as C has more elements near its mean so it will be placed 3rd
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Re: PS questions about standard deviation. [#permalink]

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08 Oct 2017, 14:39
Bunuel wrote:
Questions 1 and 9 are solved incorrectly. One of two answers for 6 is incorrect. 10 and 11 aren't solved yet, though they are relatively easy.

The hardest questions in this set are 8 and 9. Probably they are 750+ problems, so would be interesting to see the solutions for them. Also please note that I don't have the OA for 8!, only my own solution.

Good luck.

Hello Bunuel

Could you please give the best solution? I have an exam in 10 days and I'm really confused about SD
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Re: PS questions about standard deviation. [#permalink]

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08 Oct 2017, 19:54
soodia wrote:
Bunuel wrote:
Questions 1 and 9 are solved incorrectly. One of two answers for 6 is incorrect. 10 and 11 aren't solved yet, though they are relatively easy.

The hardest questions in this set are 8 and 9. Probably they are 750+ problems, so would be interesting to see the solutions for them. Also please note that I don't have the OA for 8!, only my own solution.

Good luck.

Hello Bunuel

Could you please give the best solution? I have an exam in 10 days and I'm really confused about SD

You can find solutions to each question on previous pages.

[textarea]

20. Descriptive Statistics

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Re: PS questions about standard deviation.   [#permalink] 08 Oct 2017, 19:54

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