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

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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02 Mar 2017, 08:08
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66% (01:40) correct 34% (01:40) wrong based on 185 sessions

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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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WE: Corporate Finance (Energy and Utilities)
Re: Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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02 Mar 2017, 08:22
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,..
Manager
Joined: 28 Jul 2016
Posts: 132
Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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02 Mar 2017, 10:37
Looks like correct answer is D
$$n^{3}-60$$ increments faster than other options
Senior Manager
Joined: 12 Sep 2017
Posts: 302
Re: Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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20 Jan 2019, 16:44
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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Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 434
Re: Set A consists of the the first 10 terms of a sequence. For which sequ  [#permalink]

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13 Feb 2019, 09:46
1
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.
Re: Set A consists of the the first 10 terms of a sequence. For which sequ   [#permalink] 13 Feb 2019, 09:46
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