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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
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 B, 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.
Re: Range & SD (m03q34) [#permalink]
10 Oct 2012, 04:54
In response to the first question"
Don't get confused, this is not a DS question, Review each option individually ONLY.
Which set(s) has the greatest standard deviation?
1. Set 1 consisting of 10 digits we can have endless prossibilities to have a set with 10 digits- we don't know what to choose-incorrect 2. Set 2 consisting of 10 first positive consecutive even numbers The required set will be { 2,4,6,......blah blah , 18,20} all you need to know the 10th digit i.e 20. 3. Set 3 consisting of 10 first primes The required set will be { 2,4......blah blah blah} Don't waste your time in counting the 10th prime number(unless you have mugged up ) all you need is to know the maximum value and the minimum values to find the SD in this case)
in (3) it will be definitely more than how much it will be in (2)
Answer : (C)
The question right above this post (posted by Bunuel ) is a way trickier but here you need to solve the puzzle with the digits, which is mentioned in various ACs and Bunuel's explanation is fantastic. _________________
" Make more efforts " Press Kudos if you liked my post
Standard deviation is a measure of how elements in a set are "SPREAD" out, with respect to the mean of the set. It is as simple as that. There is no need for any complication calculations. Most of the time, a visual inspection of members of the set are all that is required to compare standard deviations.
Consider the set A : 10, 12, 14, 16, 18, 20, 22, 24, 26, 28. Don't make the mistake of calculating the mean and standard deviation just yet ! Remember the GMAT is never about busy math. Just make a mental note that the members of the set are "2" units apart from the predecessor and successor.
Lets look at Set B, which consists of first 10 positive integers. B = { 1,2,3,4,5,6,7,8,9,10 } - The members of the set are "1" unit apart from its predecessor and successor. Surely the elements of this set are closer together to each other than the members of the set A = { 10, 12, 14, 16, 18, 20, 22, 24, 26, 28} .
Why ? For starters, the members of the set A are 2 units apart from each other.
II. Set C, which consists of 10 first positive odd numbers C = { 1,3,5,7,9,11,13,15..} . These members of set C are "2" units apart from each other, hence the SD of this set exactly equal to A={10, 12, 14, 16, 18, 20, 22, 24, 26, 28}. Remember the standard deviation is about how "far or close" the members of the set are in relation to the mean. The actual members of the set matters very little, Let me explain Consider the sets X = { 1000,1001,1002} , Y = { 0,1,2}, Z= { -1,0,1}, M = { 4,5,6 } ===> Guess what, the SDs of all these sets are exactly the same. Do you see a pattern here ? !!!
III D - Set of first 10 primes = { 1, 3, 5, 7, 11, 13...} Ok. We have a winner here. Clearly the members of this set are farther away from each other than the members of set "A". We are done ! _________________
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Last edited by hafizkarim on 11 Oct 2013, 11:01, edited 3 times in total.
standard deviation depends on how wide spread a given set is. set B = {1,2,3,4,5,6,7,8,9,10} is less widespread than A. so, standard deviation is less than A. spread of set C={1,3,5,7,9,11,13,15,17,19} is same as A. so, same standard deviation. set D={2,3,5,7,11,13,17,19,23,29}is more wide spread than A. so, standard deviation is more than A.