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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Kudos [?]: 1957 , given: 397

numbers in data set S have a standard deviation of 5 [#permalink]
Expert's post 00:00

Question Stats: 92% (00:21) correct 7% (00:34) wrong based on 26 sessions
The numbers in data set S have a standard deviation of 5. If a new data set is formed by adding 3 to each number in S, what is the standard deviation of the numbers in the new data set?

A 2
B 3
C 5
D 8
E 15

Practice Questions
Question: 12
Page: 460
Difficulty: medium
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 122

Kudos [?]: 1957 , given: 397

Re: numbers in data set S have a standard deviation of 5 [#permalink]
Expert's post
Solution

The new data set is formed by adding the same number, 3, to each number in data set S. Thus, the mean of the numbers in the new data set is 3 more than the mean of the numbers in S, but the spread of the numbers in the new data set about the mean of the numbers in the new data set is the same as the spread of the numbers in S about the mean of the numbers in S.

Because the standard deviation of the numbers in S is 5, the standard deviation of the numbers in the new data set is also 5. The correct answer is Option C.
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Sandy
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Kudos [?]: 1954  , given: 17

Re: numbers in data set S have a standard deviation of 5 [#permalink]
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Expert's post
sandy wrote:
The numbers in data set S have a standard deviation of 5. If a new data set is formed by adding 3 to each number in S, what is the standard deviation of the numbers in the new data set?

A 2
B 3
C 5
D 8
E 15

Standard deviation measures how spread apart (dispersed) the numbers in a set are.
So, adding 5 to each value in the set does not affect the standard deviation.

Here's an example:
Let's say set A = {2, 3, 6, 7, 7}
The mean of set A is 5
Let's see how far each value in set A is away from the mean of 5
2 is 3 away from the mean of 5
3 is 2 away from the mean of 5
6 is 1 away from the mean of 5
7 is 2 away from the mean of 5
7 is 2 away from the mean of 5

Now let's add 5 to each value in set A.
We get a NEW set: {7, 8, 11, 12, 12}
The mean of this new set is 10
Let's see how far each value in the set is away from the mean of 10
7 is 3 away from the mean of 10
8 is 2 away from the mean of 10
11 is 1 away from the mean of 10
12 is 2 away from the mean of 10
12 is 2 away from the mean of 10

As you can see, both sets have the same dispersion.
So, the standard deviations of the two sets, {2, 3, 6, 7, 7} and {7, 8, 11, 12, 12} are EQUAL

So, to answer the ORIGINAL question, the standard deviation of the new set will be 5 (the same as it was with the original set)

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Re: numbers in data set S have a standard deviation of 5   [#permalink] 07 Mar 2018, 10:10
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