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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