M03-34

Question

Which of the following sets has a 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 the first 10 positive integers
 
II. Set C, which consists of the first 10 positive odd numbers
 
III. Set D, which consists of the first 10 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

Bunuel · Accepted Answer

Official Solution:

Which of the following sets has a 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 the first 10 positive integers
 
II. Set C, which consists of the first 10 positive odd numbers
 
III. Set D, which consists of the first 10 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 is a measure of the variation of the data points from the mean, a measure of how widespread a given set is. When the standard deviation is low, the data points tend to be close to the mean, while a high standard deviation implies that the data is spread out over a broader range of values.
 
Now, it's clear that 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 is equal to the standard deviation of set A. An important property to note is that  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, 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

vyomb · Answer

can be evaluated like..

sigma set A= 18

sigma set B = 9

sigma set C=18

sigma set D= 28

So correct answer is option C

Desertchampion · Answer

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.

testtakerstrategy · Answer

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???

Bunuel · Answer

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 
     Theory   
 Statistics Made Easy - All in One Topic! 
 GMAT Statistics 101 
 Math: Standard Deviation 
 How to Quickly Solve Standard Deviation Questions on the GMAT 
     Questions   
 Standard Deviation Problems 
 DS Questions 
 PS Questions

For more check:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

akt715 · Answer

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

Bunuel · Answer

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.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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M03-34

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