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The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6

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The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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Updated on: 22 Jun 2016, 05:44
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The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S consisting of all those elements in S which are more than two but less than three standard deviations away from the arithmetic mean of S, what could be equal to the standard deviation of S?

A) 0.54
B) 0.77
C) 0.82
D) 0.97
E) 1.62

Originally posted by riteshpatnaik on 21 Jun 2016, 21:37.
Last edited by Bunuel on 22 Jun 2016, 05:44, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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02 Aug 2016, 21:53
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riteshpatnaik wrote:
The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S consisting of all those elements in S which are more than two but less than three standard deviations away from the arithmetic mean of S, what could be equal to the standard deviation of S?

A) 0.54
B) 0.77
C) 0.82
D) 0.97
E) 1.62

Imagine them on number line:

-2.22 ............. - 1.96 ............... - 1.68 ...........................................0 .......................................... 1.62 ..................... 1.94 .................... 2.16

Mean is 0.

Each of these elements is more than 2 SD away from mean. 1.62 is closest to mean 0 but it is more than 2 SD away from 0.
So 1 SD will be less than 1.62/2 = .81.

Similarly, each of these elements is less than 3 SD away from mean. - 2.22 is farthest from mean 0 but it is less than 3 SD away.
So 1 SD will be more than 2.22/3 = .74

There is only one options between .74 and .81 and that is .77.
Answer (B)
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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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22 Jun 2016, 04:06
Answer is D : 0.97.

(Bro, I'm not sure about this question, doesn't seems close to any questions i've seen so far, so giving it a shot)

I'm using the second part of the statement about the standard deviation. Using the standard Gaussian curve centered around Y axis with mean zero, +/- 2 sigma = 95% and +/-3 sigma = 99%, so the Standard deviation of the set should be between these, hence 0.97 or 97%

(Share a kudo's if you like the explanation)
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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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22 Jun 2016, 05:48
riteshpatnaik wrote:
The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S consisting of all those elements in S which are more than two but less than three standard deviations away from the arithmetic mean of S, what could be equal to the standard deviation of S?

A) 0.54
B) 0.77
C) 0.82
D) 0.97
E) 1.62

Edited the question.

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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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02 Aug 2016, 10:37
riteshpatnaik wrote:
The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S consisting of all those elements in S which are more than two but less than three standard deviations away from the arithmetic mean of S, what could be equal to the standard deviation of S?

A) 0.54
B) 0.77
C) 0.82
D) 0.97
E) 1.62

Quote:
Hello Experts:
Can you please provide answer to this question?
Thanks in advance.
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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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02 Aug 2016, 10:47
Hi Yosita,

Let me know if this explanation is not clear enough.

Answer is D : 0.97.

(Bro, I'm not sure about this question, doesn't seems close to any questions i've seen so far, so giving it a shot)

I'm using the second part of the statement about the standard deviation. Using the standard Gaussian curve centered around Y axis with mean zero, +/- 2 sigma = 95% and +/-3 sigma = 99%, so the Standard deviation of the set should be between these, hence 0.97 or 97%
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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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02 Aug 2016, 21:15
This is a fairly straightforward question that can be solved quickly by just applying the options

We are provided with Mean, m= 0
and T = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S

T consists of all those elements in S that are more than 2 but less than 3 SDs away from the arithmetic mean of S

If an element is 1 SD away from the mean, we can write it as either m + SD or m - SD
Similarly, if an element is 2 SDs away from the mean, we can write it as either m + 2*SD or m - 2*SD

So, if these elements lie within 2 and 3 SDs of mean, m=0
we can find which one of these values of SD satisfies each value within T

Only SD = 0.77 does

Answer : B
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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6  [#permalink]

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22 Sep 2017, 08:43
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Re: The arithmetic mean of set S is zero. If T = {-2.22; -1.96; -1.68; 1.6 &nbs [#permalink] 22 Sep 2017, 08:43
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