Question

Show using an example the effect, if any, on the standard deviation of adding a data value to a set of data that is equivalent to the mean.

Not quite sure what "standard deviation of adding a data value to a set of data that is equivalent to the mean," means.
An example would also help... thanks.

Answer 1

Wait, what I'm understanding is that it's asking you just to add another data value that is the equal to the mean to your current set of data?

Also, the example and effect that it's asking to give can be shown by random numbers, right?

Answer 2

Ok, I think I got it now. So I have 5 numbers
(2, 3, 5, 8, and 13).
If the mean of these numbers is 6.2 (standard deviation is 3.77), based on the question I would then add the mean (6.2) to my 5 numbers (making it 6 numbers), and then recalculate the mean again, and also the standard deviation?
So the standard deviation after would be 3.44.
The answer would be that the deviation decreased?

Answer 3

You are correct. The standard deviation measures the variation from the mean. So if you add values that are close to or equal to the mean, that would decrease that variation or deviation from the mean.
Your example is a good one.

Answer 4

thank you :)