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# PS questions about standard deviation.

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Math Expert
Joined: 02 Sep 2009
Posts: 60647

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27 Oct 2009, 16:37
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Lately, many questions were asked about the standard deviation. So I'm posting here my collection of PS on SD, plus some tips about it.

A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated helps in understanding the concept.
B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on combinatorics), actually you may see none, so do not spend too much of your preparation time on it, it's better to concentrate on issues you'll definitely face on G-day.

Many questions below are easy, some are tough, but anyway they are good to master in solving SD problems. I'll post OA after some discussions. Please provide your way of thinking along with the answer. Thanks.

Here we go:

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-set-of-dat ... 47858.html

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-certain-li ... 59504.html

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/for-a-certai ... 28661.html

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}

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/which-of-the ... 18777.html

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/which-of-the ... 62888.html

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%

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-certain-ch ... 43982.html

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}

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/which-of-the ... 18778.html

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

SOLUTION IS HERE: https://gmatclub.com/forum/ps-questions ... ml#p664302

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/e-is-a-colle ... 99774.html

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-a-certain ... 30542.html

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-arithmet ... 29117.html

CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:
1. Find the mean, m, of the values.
2. For each value xi calculate its deviation (xi-m) from the mean.
3. Calculate the squares of these deviations.
4. Find the mean of the squared deviations. This quantity is the variance.
5. Take the square root of the variance. The quantity is th SD.

TIPS:
1. |Median-Mean| <= SD.

2. Variance is the square of the standard deviation.

3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.

4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.

6. If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

7. If we increase or decrease each term in a set by the same percent:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.

9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.

You can also check collection of DS questions of SD at: http://gmatclub.com/forum/ds-questions- ... 85896.html

20. Descriptive Statistics

For more check:
ALL YOU NEED FOR QUANT ! ! !
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04 Nov 2009, 17:45
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14

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

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27 Oct 2009, 20:43
12
2
Bunuel wrote:
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

(D) I and II only

Anything added/deducted to the set elements or the set elements deducted from anything results in no change in SD.

I. Deduct 2 from each of the elements in set result I. i.e. {r-2, s-2, t-2}
II. Deduct each set elements from s. The new set elements in II i.e. {0, s-t, s-r} result.
III. Taking the absolute value of the set elements is not the same as deducuting or adding the same. This act would not change the SD if all set elements have the same sign (+ve or -ve).

Suppose s = 5 and r = 6 and t = 7, {|r|, |s|, |t|} and {s, r, t} have same SD.
If s = -5 and r = -6 and t = -7, {|r|, |s|, |t|} and {s, r, t} have same SD.
If s = -5 and r = 6 and t = 7, {|r|, |s|, |t|} and {s, r, t} have different SD.

III is not always a true case.
##### General Discussion
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Joined: 29 Aug 2007
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27 Oct 2009, 20:32
8
3
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.
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15 May 2010, 21:18
8
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.
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27 Oct 2009, 21:09
7
7
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.
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Joined: 02 Sep 2009
Posts: 60647

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02 Jan 2010, 13:37
7
5
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.
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Posts: 1881

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18 Dec 2009, 09:07
6
9
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.
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Joined: 02 Sep 2009
Posts: 60647

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31 Oct 2010, 18:00
5
3
santy wrote:
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?

Q#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

Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets:

1. {1, 1, 1, 5} --> mean=2 --> |mean-x|=(1, 1, 1, 3);
2. {1, 1, 3, 5} --> mean=2.5 --> |mean-x|=(1.5, 1.5, 0.5, 2.5);
3. {1, 1, 5, 5} --> mean=3 --> |mean-x|=(2, 2, 2, 2);
4. {1, 3, 3, 5} --> mean=3 --> |mean-x|=(2, 0, 0, 2);
5. {1, 3, 5, 5} --> mean=3.5 --> |mean-x|=(2.5, 0.5, 1.5, 1.5);
6. {1, 5, 5, 5} --> mean=4 --> |mean-x|=(3, 1, 1, 1).

CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:
1. Find the mean, $$m$$, of the values.
2. For each value $$x_i$$ calculate its deviation ($$m-x_i$$) from the mean.
3. Calculate the squares of these deviations.
4. Find the mean of the squared deviations. This quantity is the variance.
5. Take the square root of the variance. The quantity is th SD.

Expressed by formula: $$standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(m-x_i)^2}{N}}$$.

You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values.

Solutions and OA's for other questions are on previous pages.

Hope it's clear.
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27 Oct 2009, 20:25
3
Bunuel wrote:
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

x - 2sd = 58
x + 3sd = 98

SD = 8 and Mean (x) = 74 in A.
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28 Oct 2009, 14:35
3
3
Thanks Bunuel.

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

The mean of the set is 4.
sqrt[((0-4)^2+(2-4)^2+(6-4)^2+(8-4)^2)/5] = sqrt[(16+4+4+16)/5] = sqrt(40/5) = sqrt(8)

The mean of set 0,8 is 4. Std.dev. is sqrt[(0-4)^2+(8-4)^2/2]=sqrt(8). Answer is E.

Bunuel wrote:

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

E. If the set contained only 6 it's standard deviation would be 0. Since it is positive we can reduce the std.dev. by adding to integers equal to the mean - so answer is E.

Bunuel wrote:
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

2 eq in 2 unknowns. Let x denote mean and let y denote std.dev.

58 = x - 2y <=> x= 58 + 2y (1) AND
98 = x + 3y <=> 98 = 58+5y <=> y=8. Insert into (1) to get x=58+2*8= 74.

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}

A good way to go about these questions is to look for the range of the set compared to the number of elements in the set. Ceteris paribus it holds that the higher the range - the higher the std.dev and the higher the number of elements - the lower the std.dev. A is the only set with a range of 5 and only 3 numbers. Furthermore none of the numbers represent the average (0) and therefore all contribute to the std.dev. Answer is A.

Bunuel wrote:
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

The absolute value of the numbers doesn't matter since it is the differences to the mean that enters into the std.dev. Thus I is the same as in the Q. The set in 2 is the set (s,s,s) subtracted by (s,r,t). This gives the same std.dev. as in set {s,r,t} (If you're in doubt try plugging in numbers. In III there is clearly a difference between the set {-1,1,1} and {1,1,1} so this does not necessarily have the same std.dev as {s,r,t}. The answer is D.

Bunuel wrote:
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%

I am little uncertain about the meaning of this question. I will assume that you mean that 68% of the distribution lies one standard deviation above the mean (alternative interpretation is that 68% of the distribution lies within 1 std.dev from the mean).

The total mass of the distribution is 100%. Just subtract 68% from the total mass to get this rest = 32%. Answers is B.

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}

Use the same principle I described above. All sets have 5 numbers. E have the larges range, and D comes in second. A has the third largest range and greater dispersion among numbers so answer is A.

OK, gotta hit the sack now. Thanks again for the questions Bunuel.
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Posts: 60647

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21 Mar 2012, 06:15
3
@ Bunuel

please explain the logical understanding/ difference between questions 10 and 11.
my doubt for q-11 is m getting

value=13.5+ 3= 16.5 and 10.5 so the value should be between 10.5 and 16.5,

however the options and the corresponding OA just confuses me.

pls explain

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

Value is more than 2.5SD from the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 20-7.5=12.5 or more than 20+7.5=27.5.

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

The value which is exactly two SD less than the mean is: mean-2*SD=13.5-2*1.5=10.5.

Hope it's clear.
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27 Oct 2009, 21:33
2
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.
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30 Oct 2009, 00:09
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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.

Thats a real tricky question and is of 750+ level. Did not think that some of the SDs are of equal value.
Revised to 4 in B.
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08 Jun 2010, 08:48
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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.

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19 Jun 2012, 07:53
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:@Ritesh Gupta: Let me try to explain this to you.

consider a straight line that represents the mean (m). and lets consider S.D d as one unit. so you have m+d above the line m and m-d below the line m. Now given that 68% lies within one standard deviation from mean, that means 68% = m+d and m-d, which means 34% each. Next, remaining 32% (100-68) is above m+d and below m-d, again equally distributed, hence, 16% each.

Thus, if you graphically visualize, the question is asking you, (m+d) + (m-d) + below (m-d) = 34 + 34 + 16 = 84.

I hope its clear!
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11 Jul 2012, 01:58
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dianamao wrote:
Bunuel wrote:
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|}

How is II. {0, s-t, s-r} derived?

Note that:
If we add or subtract a constant to each term in a set: SD will not change.

Changing the signs of the element of a set (multiplying by -1) has no effect on SD.

Now, multiply {s, r, t} by -1 to get {-s, -r, -t}. According to the above these two sets have the same standard deviation.

Next, add s to each term to get {0, s-r, s-t}, again according to the above {0, s-r, s-t} and {-s, -r, -t} have the same standard deviation.

So, {s, r, t}, {-s, -r, -t} and {0, s-r, s-t} have the same standard deviation.

Hope it's clear.
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27 Oct 2009, 20:14
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Bunuel wrote:
A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated helps in understanding the concept.

B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on combinatorics), actually you may see none, so do not spend too much of your preparation time on it, it's better to concentrate on issues you'll definitely face on G-day.

Good work.
1. I agree with point A.
2. I do not fully agree with point B. Agree with time saving part is ok but want to work on understanding the SD issues/questions in more detail as well. I cannot depend on praying for no SD questions, relying on chance.
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27 Oct 2009, 20:23
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GMAT TIGER wrote:
Bunuel wrote:
A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated helps in understanding the concept.

B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on combinatorics), actually you may see none, so do not spend too much of your preparation time on it, it's better to concentrate on issues you'll definitely face on G-day.

Good work.
1. I agree with point A.
2. I do not fully agree with point B. Agree with time saving issue but still work on understanding the SD issues/questions too. I cannot depend on praying for no SD question as I do not want to take a chance.

GMAT TIGER point B no way means that one should't work on SD issues, not at all. The point B. means that taking into account the probability of getting SD on real GMAT one should spread the time wisely. Right the way you've mentioned: time saving is the key issue here.
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27 Oct 2009, 21:30
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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.

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