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# For the sets of numbers above, which of the following is true?

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
For the sets of numbers above, which of the following is true?  [#permalink]

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16 Jun 2015, 03:42
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:17) correct 6% (00:53) wrong based on 112 sessions

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Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Kudos for a correct solution.

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For the sets of numbers above, which of the following is true?  [#permalink]

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Updated on: 16 Jun 2015, 08:16
1
1
Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

Note : Both Set A and Set B are in arithmetic progression

Mean(Set A) = 5 : Median(Set A) = 5
Mean(Set B) = 10 : Median(Set B) = 10

Let's compute Standard Deviation(S.D).

S.D of an arithmetic progression :: |d| * $$\sqrt{(N^2-1)/12}$$
d= common difference and N = number of terms in Arithmetic Progression

So S.D(Set A) = 2 * $$\sqrt{(5^2-1)/12}$$ = 2 * $$\sqrt{(24/12)}$$ = 2$$\sqrt{2}$$
S.D(Set B) = 2$$\sqrt{2}$$ ( Since the common difference and Number of terms is same as Set A)

I. The mean of Set B is greater than the mean of Set A. (true)
II. The median of Set B is greater than the median of Set A. (true)
III. The standard deviation of Set B is greater than the standard deviation of Set A. (False)

So I and II are true

Ans : B

Originally posted by ManojReddy on 16 Jun 2015, 05:13.
Last edited by ManojReddy on 16 Jun 2015, 08:16, edited 1 time in total.
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Re: For the sets of numbers above, which of the following is true?  [#permalink]

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16 Jun 2015, 05:31
Bunuel wrote:
Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Kudos for a correct solution[/b]

Please note: When all the terms of any set of terms are separated by equal value then the MEAN will be same as MEDIAN

Checking I :
Mean of A = Sum of {1, 3, 5, 7, 9} / 5 OR Median of {1, 3, 5, 7, 9}= 5
Mean of B = Sum of {6, 8, 10, 12, 14} / 5 OR Median of {6, 8, 10, 12, 14}= 10
Mean of B > Mean of A TRUE

Checking II :
Mean of A = Sum of {1, 3, 5, 7, 9} / 5 OR Median of {1, 3, 5, 7, 9}= 5
Mean of B = Sum of {6, 8, 10, 12, 14} / 5 OR Median of {6, 8, 10, 12, 14}= 10
Median of B > Median of A TRUE

Checking III :
CONCEPT: Standard Deviation is dependent of the separation of terms in any set and the number of terms in the same set
Set A = Separation between any two consecutive terms of {1, 3, 5, 7, 9} = 2 and No of Terms = 5
Set B = Separation between any two consecutive terms of {6, 8, 10, 12, 14} = 2 and No of Terms = 5

i.e. Standard Deviation of Set A = Standard Deviation of Set B i.e. "FALSE"

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For the sets of numbers above, which of the following is true?  [#permalink]

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16 Jun 2015, 05:45
1
Bunuel wrote:
Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Kudos for a correct solution.

Set A and B are evenly spaced. Therefore mean = median for both. Set A median, mean = 5 and Set B median, mean = 10. Statement 1 and 2 hold true. Standard Deviation is the same for both sets A and B. Therefore III. is incorrect.

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Re: For the sets of numbers above, which of the following is true?  [#permalink]

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16 Jun 2015, 06:50
1
I. Yes: mean of set A is 5, mean of set B 10
II Yes: Median of set A is 5, median of set B is 10.
III No: as the range of both the set is same.

Ans is B

(for info : both set are in AP so mean = median)
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Re: For the sets of numbers above, which of the following is true?  [#permalink]

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16 Jun 2015, 07:59
1
Bunuel wrote:
Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Kudos for a correct solution.

Analyze each statement:
I. The mean for Set A is (9+1)/2 while the mean for Set B is (6+14)/2. Mean for Set A = 5 while Mean for Set B = 10. True!
II. Median of Set A is clearly 5 (odd numbered group, pick the middle number) and Set B is 10. True!
III. Numbers are two digits apart. The SD is the same for both Set A and Set B. False.

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Re: For the sets of numbers above, which of the following is true?  [#permalink]

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16 Jun 2015, 10:13
Bunuel wrote:
Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Kudos for a correct solution.

Solution -

I. Mean of B(10) greater than mean of A(5). Sufficient.
II. Median of B(10) is greater then median of A(5). Sufficient.

III. Set A = {1, 3, 5, 7, 9} , The values deviated from Mean(5) is {4,2,0,2,4}
Set B = {6, 8, 10, 12, 14}, The values deviated from Mean(10) is {4, 2, 0, 2, 4}.

Hence the Standard Deviation is same for both the sets. In Sufficient.

ANS B.

Thanks,

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Posts: 163
Re: For the sets of numbers above, which of the following is true?  [#permalink]

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18 Jun 2015, 04:26
[quote="Bunuel"]Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Mean A = \frac{(1+3 + 5 + 7 + 9)}{5} = 5
Mean B = \frac{(6+ 8 + 10 + 12 + 14)}{5} = 10

Median A = 5
Median B = 10

Statement 1 : TRUE
Mean B > Mean A (Calculated Above)

Statement 2 : TRUE
Median B > Median A

Statement 3 - Incorrect. Mean of B = Mean of A
Keeping Gmat time constraint in view lets not calculate Standard deviation. Standard deviation is spread from Mean. since number of elements are same, we can (approximately) compare std deviation using spread
Mean of A is 5, so maximum spread is 4 (Since smallest element is 1 , 4 unit away from mean 5 similarly 9 max spread is 4)
Mean of B is 10, so max spread is 4

Hence Option B is correct
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Posts: 59587
Re: For the sets of numbers above, which of the following is true?  [#permalink]

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22 Jun 2015, 06:59
Bunuel wrote:
Set A: 1, 3, 5, 7, 9
Set B: 6, 8, 10, 12, 14

For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

On a number line, both sets of numbers are evenly spaced in increments of 2. The only difference between the sets is that Set B is shifted 5 to the right of Set A.

Thus,

I. TRUE. Mean of B = Mean of A + 5.
II. TRUE. Median of B = Median of A + 5
III. FALSE. Std. Dev. of B = Std. Dev. of A

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Re: For the sets of numbers above, which of the following is true?   [#permalink] 22 Jun 2015, 06:59
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