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# M03-34

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Re: M03-34 [#permalink]
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The standard deviation measures how far a set of values are from the average of that set.

In order to calculate the standard deviation of a set, do the following:
1) Find the mean of the set
2) Subtract each term from the mean
3) Square each number obtained in step 2
4) Find the mean of the values in step 3
5) Take the square root of the mean in step 4

Now, we won't be expected to do this on the GMAT, but we will be expected to recognize some patterns.
Back to the question:

set A={10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

I. Set B={1,2,3,4,5,6,7,8,9,10}
The terms in this set are closer to each other than the terms in set A, therefore the standard deviation of set B is less than the standard deviation of set A.

II. Set C={1,3,5,7,9,11,13,15,17,19}
The terms in this set are as spaced out as the terms in set A, therefore the standard deviation of set C is the same as the standard deviation of set A.

III. Set D={2,3,5,7,11,13,17,19,23,29}
The terms in this set are more spread out than the terms in set A, therefore the standard deviation of set D is greater than the standard deviation of set A.

The answer is C.
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Re: M03-34 [#permalink]
Is it accurate to say that "as a set's range increases, its standard deviation increases"?

so ANY set will have a larger standard deviation as long as its range is larger???
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Re: M03-34 [#permalink]
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testtakerstrategy wrote:
Is it accurate to say that "as a set's range increases, its standard deviation increases"?

so ANY set will have a larger standard deviation as long as its range is larger???

No, that would not be right. For example, the standard deviation of {1, 7} is 3 and the range is 6 while the standard deviation of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is approximately 2.9 and the range is 9.

20. Descriptive Statistics

For more check:
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Re: M03-34 [#permalink]
Bunuel wrote:
Official Solution:

Which of the following sets has the standard deviation greater than the standard deviation of set A={10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

I. Set B, which consists of 10 first positive integers

II. Set C, which consists of 10 first positive odd numbers

III. Set D, which consists of 10 first prime numbers

A. set B only
B. set C only
C. set D only
D. sets C and D only
E. sets B, C and D

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

Now, clearly set B={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less widespread than set A, so its standard deviation is less than the standard deviation of set A;

Set C={1, 3, 5, 7, 9, 11, 13, 15, 17, 19} is as widespread as set A, so its standard deviation equals to the standard deviation of set A (important property: if we add or subtract a constant to each term in a set the standard deviation will not change, since set A can be obtained by adding 9 to each term of set C, then the standard deviations of those sets are equal);

Set D={2, 3, 5, 7, 11, 13, 17, 19, 23, 29} is more widespread than set A, so its standard deviation is greater than the standard deviation of set A.

Answer: C

How can you say that set D is more widespread than set A , without calculating the mean.
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Re: M03-34 [#permalink]
Expert Reply
akt715 wrote:
Bunuel wrote:
Official Solution:

Which of the following sets has the standard deviation greater than the standard deviation of set A={10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

I. Set B, which consists of 10 first positive integers

II. Set C, which consists of 10 first positive odd numbers

III. Set D, which consists of 10 first prime numbers

A. set B only
B. set C only
C. set D only
D. sets C and D only
E. sets B, C and D

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

Now, clearly set B={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is less widespread than set A, so its standard deviation is less than the standard deviation of set A;

Set C={1, 3, 5, 7, 9, 11, 13, 15, 17, 19} is as widespread as set A, so its standard deviation equals to the standard deviation of set A (important property: if we add or subtract a constant to each term in a set the standard deviation will not change, since set A can be obtained by adding 9 to each term of set C, then the standard deviations of those sets are equal);

Set D={2, 3, 5, 7, 11, 13, 17, 19, 23, 29} is more widespread than set A, so its standard deviation is greater than the standard deviation of set A.

Answer: C

How can you say that set D is more widespread than set A , without calculating the mean.

A={10, 12, 14, 16, 18, 20, 22, 24, 26, 28}
D={2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

Set A is a set of 10 consecutive even integers, so the difference between consecutive terms is 2.
Set D is a set of 10 consecutive prime numbers, so the average difference between consecutive terms is greater than 2.

Therefore, set D is more widespread than set A.
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Re: M03-34 [#permalink]
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
Re: M03-34 [#permalink]
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