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
5Let's see how far each value in set A is away from the mean of
52 is
3 away from the mean of
53 is
2 away from the mean of
56 is
1 away from the mean of
57 is
2 away from the mean of
57 is
2 away from the mean of
5Now 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
10Let's see how far each value in the set is away from the mean of
107 is
3 away from the mean of
108 is
2 away from the mean of
1011 is
1 away from the mean of
1012 is
2 away from the mean of
1012 is
2 away from the mean of
10As 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
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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