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Bunuel
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Set A consists of the the first 10 terms of a sequence. For which sequ 02 Mar 2017, 08:08
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73% (01:39) correct 27% (01:39) wrong based on 569 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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D
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Set A consists of the the first 10 terms of a sequence. For which sequ 02 Mar 2017, 08:22
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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 02 Mar 2017, 10:37
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Looks like correct answer is D
\(n^{3}-60\) increments faster than other options
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Set A consists of the the first 10 terms of a sequence. For which sequ 20 Jan 2019, 16:44
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Bunuel
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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Set A consists of the the first 10 terms of a sequence. For which sequ 13 Feb 2019, 09:46
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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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Set A consists of the the first 10 terms of a sequence. For which sequ Updated on: 13 May 2022, 03:36
Originally posted by brianmontanaweb on 08 May 2022, 05:58.
Last edited by brianmontanaweb on 13 May 2022, 03:36, edited 2 times in total.
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Bunuel
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. \(a_n=2n+100\)

Taking only the first and last value in the set, 1 and 100, to determine the standard deviation in the set.

A and D both look the most promising for variation, so focusing on those. Eliminating B, C, and E through quick mental math.

\(a_1=1^2\) = 1
\(a_10=10^2\) = 100

A can move from 1 to 100.

\(a_1=1^3−60\) = -59
\(a_10=10^3−60\) = 940

D has the largest standard deviation between the two. D wins!
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Set A consists of the the first 10 terms of a sequence. For which sequ 08 May 2022, 07:26
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IMO D,
I did not use notebook for this one , not sure if my method was correct.
I ignored whatever was +100 or -50 in options as that is going to be same in all terms.
Also if all terms are multiplied by something S.D. is also multiplied by it and here \(n3\) is the biggest multiplication happening .
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Set A consists of the the first 10 terms of a sequence. For which sequ 12 May 2022, 23:28
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jfranciscocuencag
Bunuel
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. \(a_n=2n+100\)


Kind regards![/quote]



When finding standard daviation, addition or subtraction of same number in entire set will not influence SD. However if you multiply or divide, SD will multiply and divide in same manner.

In this case addition or subtraction of 50, 60 and 100 in elements will not change SD. so ignore such part. I hope that answers your question.

exa set1 {1,2,3} have same SD as set2 {50,51,52}(added 50 in set1)
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Set A consists of the the first 10 terms of a sequence. For which sequ 15 Jun 2025, 08:36
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