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Set N is a set of x distinct positive integers where x > 2.
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28 Jul 2018, 16:25
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Set N is a set of x distinct positive integers where x > 2.
Quantity A
Quantity B
The standard deviation of set N
The standard deviation of set N if every number in the set were multiplied by –3
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
Re: Set N is a set of x distinct positive integers where x > 2.
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12 Aug 2018, 16:17
2
Expert Reply
Explanation
“Set N is a set of x distinct positive integers where x > 2” just means that the members of the set are all positive integers different from each other, and that there are at least 3 of them.
Nothing is given about the standard deviation of the set other than that it is not zero. (Because the numbers are different from each other, they are at least a little spread out, which means the standard deviation must be greater than zero. The only way to have a standard deviation of zero is to have a “set” of identical numbers, which would be referred to as a list or a dataset because all of the elements of a proper set (in math) must be different).
In Quantity B, multiplying each of the distinct integers by –3 would definitely spread out the numbers and thus increase the standard deviation. For instance, if the set had been 1, 2, 3, it would become –3, –6, –9. The negatives are irrelevant—multiplying any set of different integers by 3 will spread them out more.
Thus, whatever the standard deviation is for the set in Quantity A, Quantity B must represent a larger standard deviation because the numbers in that set are more spread out.
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Re: Set N is a set of x distinct positive integers where x > 2.
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23 Aug 2018, 06:55
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Expert Reply
sandy wrote:
Set N is a set of x distinct positive integers where x > 2.
Quantity A
Quantity B
The standard deviation of set N
The standard deviation of set N if every number in the set were multiplied by –3
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
ASIDE: The key here is that the numbers are DISTINCT (if they weren't distinct, then the answer would be D).
Let's examine some possible sets: If set N = {1, 2, 3}, then the NEW set = {-3, -6, -9} Notice that the NEW set is MORE DISPERSED than the original set. So, the standard deviation of the NEW set is greater than that of the original set
Likewise, if set N = {0.2, 0.5 and 1.1}, then the NEW set = {-0.6, -1.5, -3.3} Notice that the NEW set is MORE DISPERSED than the original set. So, the standard deviation of the NEW set is greater than that of the original set
Likewise, if set N = {-1, 0 and 1}, then the NEW set = {3, 0, -3} Notice that the NEW set is MORE DISPERSED than the original set. So, the standard deviation of the NEW set is greater than that of the original set
Etc.
Answer: B
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