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Set A consists of the the first 10 terms of a sequence. For which sequ

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New post 02 Mar 2017, 07:08
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A
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Set A consists of the the first 10 terms of a sequence. For which sequence, in which \(a_n=x\) defines how the nth term is calculated, will set A have the greatest standard deviation?

A. \(a_n=n^2\)

B. \(a_n=2n+50\)

C. \(a_n=\frac{n}{3}\)

D. \(a_n=n^3−60\)

E. \(a_n=2n+100\)

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Re: Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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New post 02 Mar 2017, 07:22
Is it D?

By definition Standard deviation gives a measure how closely or widely spread the sequence is with respect to its mean.
Greater the difference between the numbers and mean, higher will be the Standard deviation.

Looking at the equations - we can say that third power of a number will give bigger numbers hence higher SD

A> sequence will be 1,4,9,16,25,36,49,64,81,100
B> Sequence will be 52, 54, 56, 58, 60, 62, 64, 66, 68, 70
C> Sequence will be 1/3, 2/3, 1, 4/3, 5/3, 2, 7/3, 8/3, 3, 10/3
D> Sequence will be -59, -52, -33, 4, 65, 156,...
E> Sequence will be 102, 104, 106, 108, 110, 112,..
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Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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New post 02 Mar 2017, 09:37
Looks like correct answer is D
\(n^{3}-60\) increments faster than other options
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Re: Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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New post 20 Jan 2019, 15:44
Bunuel wrote:
Set A consists of the the first 10 terms of a sequence. For which sequence, in which \(a_n=x\) defines how the nth term is calculated, will set A have the greatest standard deviation?

A. \(a_n=n^2\)

B. \(a_n=2n+50\)

C. \(a_n=\frac{n}{3}\)

D. \(a_n=n^3−60\)

E. \(a_n=2n+100\)


Hello Bunuel !

Just one question, do the numbers that are being added/subtracted have a specific meaning?

A. \(a_n=n^2\)

B. \(a_n=2n+50\)

C. \(a_n=\frac{n}{3}\)

D. \(a_n=n^3−60\)

E. \(a_n=2n+100\)[/quote]


Kind regards!
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Re: Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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New post 13 Feb 2019, 08:46
I think the numbers are arbitrary, we're not given the actual sequence so we can make up our own, like {1,2,3,5,6,7,8,9,10}.
Then plug in n=1 for first and n=10 for last term:
A) 1 to 100
B) 52 to 70
C) 1/3 to 10/3
D) -59 to 940
E) 102 to 300

We can see that D) has the largest range, and in our evenly spaced set the distance between each part of the set (the standard deviation) will be largest in D): 999/10 = 99.9 between each point.
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Re: Set A consists of the the first 10 terms of a sequence. For which sequ   [#permalink] 13 Feb 2019, 08:46
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Set A consists of the the first 10 terms of a sequence. For which sequ

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