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Manager  Joined: 29 Nov 2011
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If sets A and B have the same number of terms, is the  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 45% (01:29) correct 55% (01:16) wrong based on 561 sessions

### HideShow timer Statistics If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B?

(1) The range of set A is greater than the range of set B.
(2) Sets A and B are both evenly spaced sets.
Manager  Joined: 03 May 2014
Posts: 52
Concentration: Operations, Marketing
GMAT 1: 680 Q48 V34 GMAT 2: 700 Q49 V35 GPA: 3.6
WE: Engineering (Energy and Utilities)
If sets A and B have the same number of terms, is the  [#permalink]

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Mechmeera wrote:
I request someone to explain the above problem along with concept in detail.

Let Me try to explain you.
The Question says set A and Set B have the same number of terms.
Is SD for A> SD for B.
For comparing the SD, you don't need to actually calculate the Standard Deviation.
From Statement 1. Range of A > Range of B and from the question we know # of terms in A= # of terms in B.
so let me give you an example A{2,4,6,8,10,12} and B{2,2,2,2,10,10} Range of A is greater than B but SD is less or we can have A{2,4,6,8,10,12}, B{2,2,2,2,2,2} where SD of A> Sd of B.
Not Sufficient as we get both yes and no answer.
From Statement 2. Both are evenly space set and from the question we know # of terms in A= # of terms in B.
Again taking example of sets A{2,4,6,8,10} and B {1,2,3,4,5} so in this case SD of A> SD of B. or we can have B{2,4,6,8,10} and A{1,2,3,4,5} so in this case SD of B> SD of A.
Not sufficient as we get both yes and no answer.

Now taking A and B statement together. We know both have an equal number of terms and Range of A> Range of B and both sets have evenly spaced numbers. So for the range of A> Range of B can only be possible if numbers themselves in A are larger than numbers in B. So we know the SD of A> SD of B.
Example of sets A{2,4,6,8,10} and B {1,2,3,4,5} perfectly fits the criteria.

For SD questions, you generally don't have to calculate Standard Deviation. It is just that you have to see how far are the terms from the mean. Or you can intuitively check standard deviation (average deviation of elements from the mean)

Correct me If I am wrong.
##### General Discussion
Manager  Joined: 05 Dec 2011
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Re: If sets A and B have the same number of terms, is the standa  [#permalink]

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2
3
+1 C

1.We dont have enough info. Range could be 2, 10,10,10,20 this will have a lower SD or 2,3,3,3,3,20 will have a higher SD, same range.
2. We don't know the ranges.

Together They have the same number of terms evenly spaced, no repeats, and A has a greater range= Greater SD.
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Manager  Joined: 30 Jun 2011
Posts: 187
Re: If sets A and B have the same number of terms, is the  [#permalink]

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1
1
Yes C is correct,

Standard deviation describes how the values in a set deviate from the mean.

(1) The range of set A is greater than the range of set B.
This gives only the range i.e. outermost values but what about the other values. consider -11,0,0,0,11 and -10,-10,0,10,10
now earlier one has higher range but lower standard deviation.

(2) Sets A and B are both evenly spaced sets.
Evently spaced is oK but what is spacing since that is required to know the deviation.

Both, equal no. of numbers and A has higher range means A has no. with greater spacing so A has more Standard deviation
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Re: If sets A and B have the same number of terms, is the  [#permalink]

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1
Sets A and B have the same number of terms

Is SD of A > SD of B?

Statement 1

Range of A > Range of B

We know that they have the same number of terms but the range is not sufficient to determine the SD, the terms in between might have large or small deviations thus giving different measures of SD. Please refer to the above post for some examples

Statement 2

A,B are both evenly spaced. OK, so we know that both have the same number of terms and that they are both equally spaced, well they could even have the same components in which case the answer is NO.

Or one could be for example: 2,4,6,8 and the other 1,2,3,4 in which case the SD of the first one will be larger. Even in this case we don't know which one is A and which one is B, so this is clearly insufficient.

Both Statements together

We know that A must be larger since both are evenly spaced sets but the range of A is larger. Therefore, since they both have the same number of terms, only way that A can have a larger range is if components themselves are larger number. Therefore SD will always be larger.

Hope this helps
Cheers!
J
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If sets A and B have the same number of terms, is the  [#permalink]

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I request someone to explain the above problem along with concept in detail.
Retired Moderator S
Joined: 18 Sep 2014
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Location: India
Re: If sets A and B have the same number of terms, is the  [#permalink]

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sahil7389 wrote:
Mechmeera wrote:
I request someone to explain the above problem along with concept in detail.

Let Me try to explain you.
The Question says set A and Set B have the same number of terms.
Is SD for A> SD for B.
For comparing the SD, you don't need to actually calculate the Standard Deviation.
From Statement 1. Range of A > Range of B and from the question we know # of terms in A= # of terms in B.
so let me give you an example A{2,4,6,8,10,12} and B{2,2,2,2,10,10} Range of A is greater than B but SD is less or we can have A{2,4,6,8,10,12}, B{2,2,2,2,2,2} where SD of A> Sd of B.
Not Sufficient as we get both yes and no answer.
From Statement 2. Both are evenly space set and from the question we know # of terms in A= # of terms in B.
Again taking example of sets A{2,4,6,8,10} and B {1,2,3,4,5} so in this case SD of A> SD of B. or we can have B{2,4,6,8,10} and A{1,2,3,4,5} so in this case SD of B> SD of A.
Not sufficient as we get both yes and no answer.

Now taking A and B statement together. We know both have an equal number of terms and Range of A> Range of B and both sets have evenly spaced numbers. So for the range of A> Range of B can only be possible if numbers themselves in A are larger than numbers in B. So we know the SD of A> SD of B.
Example of sets A{2,4,6,8,10} and B {1,2,3,4,5} perfectly fits the criteria.

For SD questions, you generally don't have to calculate Standard Deviation. It is just that you have to see how far are the terms from the mean. Or you can intuitively check standard deviation (average deviation of elements from the mean)

Correct me If I am wrong.

Thanks for the simple solution.
Kudos for you. Senior Manager  G
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If sets A and B have the same number of terms, is the  [#permalink]

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1
Good question.

Statement 1: very tempting to be sufficient, but not to be so.

In GMAT, always we have to try to break condition, as it is very easy to prove the condition

Say both A and B have 100 terms.
case 1:
A: {1,2,3,4......100}
B: {50,50,50..50} = SD = 0 , in this case, S.D of A > S.D of B

case 2(breaking case):
A: {1,2,3,4....100}
B:{1,98,98,98,98..98} => S.D of B is greater than that of A

two cases, insufficient

Statement 2: cleary insufficient, as we dont know which is more evenly spaced, is it A or B, accordingly bigger SD will be decided

1+2
given range of A > range of B, so A is more evenly spaced than B, so SD of A > SD of B => (C)
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Re: If sets A and B have the same number of terms, is the  [#permalink]

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Smita04 wrote:
If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B?

(1) The range of set A is greater than the range of set B.
(2) Sets A and B are both evenly spaced sets.

statement 1 alone is insufficient as there can be many scenario for example set A can be {1,2,9} and set B can be {11,12,13}
then standard deviation of set A is greater .
But when A is {1,1,3} and set B is {11,15,19} then it is insufficient .

Statement 2 is insufficient as it does not tell us anything about individual set

Together they are sufficient

Let us take two sets
Set A {1,3,5}
Set B {11,12,13}
Now range of set A is greater than that of set B
Mean is 3 of set A mean is 12 of set B .
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Manager  S
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Re: If sets A and B have the same number of terms, is the  [#permalink]

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While the ranges of two different sets can sometimes help to indicate their relative standard deviation, more information is needed in this case.
Quote:
Statement (1) tells you that the range of A is larger than the range of set B, but it does not guarantee that the standard deviation will be bigger. If Set A were (5, 10,10,10,10,15) it would have a range of 10 and a fairly small standard deviation as most terms are the same as the average. Set B could be the following (5,5,5,14,14,14) which would have a smaller range of 9 but a clearly larger standard deviation. Statement 1 is not sufficient as numerous scenarios are possible.

Quote:
Statement (2) is clearly insufficient by itself as nothing is known about the values in the sets. Taking the statements together, it is known that there are two evenly spaced sets with the same number of terms and A has a bigger range than B. This guarantees that A must have a higher dispersion around the mean and thus a higher standard deviation. Answer is (C), both statements together are sufficient.

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If sets A and B have the same number of terms, is the  [#permalink]

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Smita04 wrote:
If sets A and B have the same number of terms, is the standard deviation of set A greater than the standard deviation of set B?

(1) The range of set A is greater than the range of set B.
(2) Sets A and B are both evenly spaced sets.

$$\# A = \# B$$

$${\sigma _A}\mathop > \limits^? {\sigma _B}$$

$$\left( 1 \right)\,\,{R_A} > {R_B}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{A = }}\left\{ {0,1} \right\}\,,\,\,B = \left\{ {0,0} \right\}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,\left\{ \matrix{ {\rm{A = }}\left\{ {0,0,0,10} \right\}\,\, \hfill \cr B = \left\{ {0,0,9,9} \right\}\,\, \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$

$$\left( 2 \right)\,\,{\rm{finite}}\,\,{\rm{APs}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{A = }}\left\{ {0,2,4} \right\}\,,\,\,B = \left\{ {0,1,2} \right\}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,{\rm{A = }}\left\{ {0,1,2} \right\}\,,\,\,B = \left\{ {0,2,4} \right\}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,{\rm{distance}}\,\,{\rm{between}}\,\,{\rm{terms}}\,\,{\rm{and}}\,\,{\rm{mean}}\,\,{\rm{in}}\,\,A\,\,{\rm{is}}\,\,{\rm{larger}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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