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.
_________________

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)

Answer: C

Cheers,
Brent
_________________

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.