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# Which of the following properly ranks the sets in terms of their stand

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Math Expert
Joined: 02 Sep 2009
Posts: 53709
Which of the following properly ranks the sets in terms of their stand  [#permalink]

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10 Apr 2018, 21:56
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Difficulty:

15% (low)

Question Stats:

81% (00:53) correct 19% (00:36) wrong based on 44 sessions

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Set A: {1, 3, 5, 7, 9}

Set B: {102, 103, 104, 105, 106}

Set C: {-15, -12, -9, -6, -3}

Which of the following properly ranks the sets in terms of their standard deviation, from greatest to least?

A. B, A, C
B. B, C, A
C. A, C, B
D. C, B, A
E. C, A, B

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Re: Which of the following properly ranks the sets in terms of their stand  [#permalink]

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10 Apr 2018, 23:29
Bunuel wrote:
Set A: {1, 3, 5, 7, 9}

Set B: {102, 103, 104, 105, 106}

Set C: {-15, -12, -9, -6, -3}

Which of the following properly ranks the sets in terms of their standard deviation, from greatest to least?

A. B, A, C
B. B, C, A
C. A, C, B
D. C, B, A
E. C, A, B

We'll show two approaches.

The first is Logical, and is based on an intuitive understanding of the term 'standard deviation'.
The standard deviation measures the 'spread', that is 'how far apart' the terms in a sequence are from each other.
Since the elements in C are at a distance of 3 from each other, those in B at a distance of 1 and in A at a distance of 2, our order is C >A > B.

The second approach is a (very long) equation-driven, Precise methodology.
As you can see, Logical methods are much faster...

We'll first calculate the mean of each set:
A --> 5, B--> 104, C--> -9
Next we'll calculate the differences from the mean in each set:
A --> {-4, -2, 0, 2, 4} B --> {-2, -1, 0, 1, 2} C--> {-6, -3, 0 3, 6}
Next we'll calculate the square of the differences:
A --> {16, 4, 0, 4, 16} B --> {4, 1, 0, 1, 4} C--> {36, 9, 0, 9, 36}
Next we'll calculate the average of the squares of the differences
A--> 40/5=8 B-->10/5=2 C--> 90/5=16
Finally we'll calculate the square root of the above
A--> 2*sqrt(2) B--> sqrt(2) C--> 4
So, after all that work, we get to C > A > B, same as the above.

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Re: Which of the following properly ranks the sets in terms of their stand  [#permalink]

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21 Apr 2018, 06:09
Standard deviation depends on how far the terms are from mean

Difference between mean and number is greatest in C then A and then B

#remeber standard deviation takes square of difference of number so greater the difference greater value of square

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Re: Which of the following properly ranks the sets in terms of their stand   [#permalink] 21 Apr 2018, 06:09
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