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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # For the set {6, 15, y}, the standard deviation is x. What is the stand

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Math Expert V
Joined: 02 Sep 2009
Posts: 56251
For the set {6, 15, y}, the standard deviation is x. What is the stand  [#permalink]

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Difficulty:   15% (low)

Question Stats: 77% (00:43) correct 23% (01:08) wrong based on 80 sessions

### HideShow timer Statistics For the set {6, 15, y}, the standard deviation is x. What is the standard deviation of the set {10, 19, (y + 4)}?

A. x
B. x + 4/3
C. x + 4
D. x + 12
E. Cannot be determined from the information provided

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Joined: 19 Apr 2016
Posts: 271
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Re: For the set {6, 15, y}, the standard deviation is x. What is the stand  [#permalink]

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1
Bunuel wrote:
For the set {6, 15, y}, the standard deviation is x. What is the standard deviation of the set {10, 19, (y + 4)}?

A. x
B. x + 4/3
C. x + 4
D. x + 12
E. Cannot be determined from the information provided

Note: If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant but SD will not change.

constant term added to set {6, 15, y} is 4 so the standard deviation remains x

Hence option A is correct
Hit Kudos if you liked it Manager  B
Joined: 06 Dec 2016
Posts: 243
Re: For the set {6, 15, y}, the standard deviation is x. What is the stand  [#permalink]

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If numbers in sequence increase by the same number then the standard deviation doesn't change. Therefore, the answer is A
Senior SC Moderator V
Joined: 14 Nov 2016
Posts: 1329
Location: Malaysia
For the set {6, 15, y}, the standard deviation is x. What is the stand  [#permalink]

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Bunuel wrote:
For the set {6, 15, y}, the standard deviation is x. What is the standard deviation of the set {10, 19, (y + 4)}?

A. x
B. x + 4/3
C. x + 4
D. x + 12
E. Cannot be determined from the information provided

Official solution from Veritas Prep.

While the abstraction in this problem may make it seem like the new standard deviation cannot be calculated, in fact one core rule about standard deviation should make this one straightforward. Since standard deviation is calculated based on the difference between each term and the mean, if all terms in a set shift by the same amount (here that amount is +4), the standard deviation will remain unchanged. Here, whatever the mean is will simply increase by 4, because each term will have increased by 4. And then each term will be the same distance away from the mean as it was before - the whole scale has simply moved 4 places to the right on the number line. Therefore, because the standard deviation is the same for the new set as it was for the old, the standard deviation is again exactly x.

If you add 4 to each term in the set, the deviation won't change. For instance, take the set {6, 15, 21}

Mean = (6 + 15 + 21)/3 = 14

Distance of each term = 8, 1, 7

Now add 4 to each term, new set {10, 19, 25}, mean = 18

Distance of each term = 8, 1, 7

Voila, same standard deviation

The sets {x, y, z} and {x+k, y+k, z+k} always have the same standard deviation for any value of k.
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Manager  S
Joined: 24 Sep 2018
Posts: 140
Re: For the set {6, 15, y}, the standard deviation is x. What is the stand  [#permalink]

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While the abstraction in this problem may make it seem like the new standard deviation cannot be calculated, one core rule about standard deviation makes this one straightforward.

Quote:
Since standard deviation is calculated based on the difference between each term and the mean, if all terms in a set shift by the same amount (here that amount is +4), the standard deviation will remain unchanged.

Here, whatever the mean is will simply increase by 4, because each term will have increased by 4. And then each term will be the same distance away from the mean as it was before - the whole scale has simply moved 4 places to the right on the number line.

Therefore, because the standard deviation is the same for the new set as it was for the old, the standard deviation is again exactly x.

Quote:
Take Away: Since standard deviation is calculated based on the difference between each term and the mean, if all terms in a set shift by the same amount (here that amount is +4), the standard deviation will remain unchanged.

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Please award kudos, If this post helped you in someway.  Re: For the set {6, 15, y}, the standard deviation is x. What is the stand   [#permalink] 25 Sep 2018, 23:03
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