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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Karishma

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