Data Sufficiency

There is a set of number, the mean is m, the standard deviation is R, if add a number x to this set, is r<= R?
1) x=m
2) m<x<m+R

sud21 wrote:There is a set of number, the mean is m, the standard deviation is R, if add a number x to this set, is r<= R?
1) x=m
2) m<x<m+R

seems like there is some issue in the question.
what does r refer to?

user123321

[spoiler]@sud21, couple of questions posted by you on the forum contain like 400 difficulty level SC mistakes which are easy to spot, what's the source of these questions? Do you copy the questions in full, because sometimes people may misunderstand the question stem. [/spoiler]
assumption is that r is a new standard deviation for the set of numbers containing x

this is a conceptual type q., as we should know beforehand that standard deviation is the average *measure of differences in distance* between mean and the given numbers (since it's taken as the squared difference, mean-number) in our set.

st(1) implies addition of another number, x, to the set and this new number will not increase the difference between mean and the number, but we cannot also say that it always *decrease* because we don't know the other numbers in the set. The other numbers may be the same (we are not told the set of different numbers), therefore we may have r is either smaller than R or equal. It's equal if x is one of many numbers in the set which are all the same. Sufficient

st(2) m<x<m+R implies new number,x, is different from the mean, but x is still within one standard deviation to the right. Hence x is not abnormal or radical value. Adding x to the set of numbers may either increase or decrease the new standard deviation, depending how close x's value is to mean (m). Not Sufficient.

a

sud21 wrote:There is a set of numbers, the mean is m, the standard deviation is R, if we (?) add a number x to this set, is r<= R?
1) x=m
2) m<x<m+R