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The standard deviation of which of the following is the same as the

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The standard deviation of which of the following is the same as the  [#permalink]

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New post 29 Nov 2019, 06:25
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E

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The standard deviation of which of the following is the same as the standard deviation of 1, 2, 3, 4, and 5?

I. -1, -2, -3, -4, -5

II. -1, 0, 3, 5, 7

III. 101, 102, 103, 104, 105

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only
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Re: The standard deviation of which of the following is the same as the  [#permalink]

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New post 29 Nov 2019, 07:24
rohan2345 wrote:
The standard deviation of which of the following is the same as the standard deviation of 1, 2, 3, 4, and 5?

I. -1, -2, -3, -4, -5

II. -1, 0, 3, 5, 7

III. 101, 102, 103, 104, 105

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only


Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

By looking at options we can clearly say 1 and 3 deviate equally from mean while 2 deviates more. Hence E is the correct answer.
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Re: The standard deviation of which of the following is the same as the  [#permalink]

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New post 29 Nov 2019, 07:31
Standard Deviation shows how members of a group differ from the mean value for the group.
Hence, it depends only on the difference between the various terms, the absolute values of term doesn't matter.

Rule:
1) if same number is added or subtracted from a set, the Standard deviation remains the same
Hence, 101, 102, 103, 104, 105 has the same SD of 1, 2, 3, 4, and 5.
2) if k is multiplied to all terms of a set, the new SD of set = |k|* original SD
I. -1, -2, -3, -4, -5 : SD will be |-1|SD of 1, 2, 3, 4, and 5
hence, both sets have same SD

Whereas, II has many irregularities, hence difference SD

Answer is E

rohan2345 wrote:
The standard deviation of which of the following is the same as the standard deviation of 1, 2, 3, 4, and 5?

I. -1, -2, -3, -4, -5

II. -1, 0, 3, 5, 7

III. 101, 102, 103, 104, 105

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only

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Re: The standard deviation of which of the following is the same as the   [#permalink] 29 Nov 2019, 07:31
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