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

Question

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

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

KarishmaB · Accepted Answer

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)

Senthil1981 · Answer

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)

Bunuel · Answer

Edited the question. PLEASE READ CAREFULLY AND FOLLOW: rules-for-posting-please-read-this-before-posting-133935.html

yosita18 · Answer

Senthil1981 · Answer

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%

ronny123 · Answer

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

JeffTargetTestPrep · Answer

Since the mean of set S is zero, the negative values in set T are between zero – 3SD and zero – 2SD. Similarly, the positive values in set T are between zero + 2SD and zero + 3SD.

Let’s test the answer choices:

A) 2SD = 2 × 0.54 = 1.08 and 3SD = 1.62 => This is an invalid case because for example, -2.22 is not between -1.62 and -1.08.

B) 2SD = 2 × 0.77 = 1.54 and 3SD = 2.31 => This is a valid case because every element in set T is between -2.31 and -1.54 or between 1.54 and 2.31.

We don’t need to check the other answer options because there can be only one correct answer.

Answer: B

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

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My Rewards