Set A has n integers. Arithmetic mean is m. standard

Question

Set A has n integers. Arithmetic mean is m. standard deviation is R. Set B has all the elements of A and x. if standard deviation of B is r, is r < R? 
(1) x = m 
(2) m <= x <= m+R

Please kindly provide explanation for the above question.

bmwhype2 · Answer

same here. value of x determines whether SD is bigger in set B.
Statement 1 says A=X. SD=same

vshaunak@gmail.com · Answer

Should be 'E'.

Stmt1:
All the elements of set A can be zero.
Then m=0, R=0, x=0
In this case r=R

If all elements of set A are not zero and x=m, std dev of set B would be less than that of set A. i.e r < R
Use formula from https://en.wikipedia.org/wiki/Standard_deviation
So Insuff

Stmt2:
m <= x <= m+R
Same expln as in stmt1
Insuff

Taking them together
x=m, all elements of set A are zero ====> R = r
x=m, all elements of set A are not zero ====> r < R
Still insuff

bmwhype2 · Answer

argh.

good catch.

goalsnr · Answer

I picked A . Now Iam eagerly waiting for the OA .

az780 · Answer

Thanks everyone for discussion OA is A.

(1) x = m
R^2 = ((a1-m) + (a2 - m) + (an-m))/n
r^2 = (R^2*n + (m-m))/n+1 => R^2*n /n+1

So, R^2*n /n+1<R^2 => n /n+1<1 => suf
If all elements in A equal 0, then R = 0, r = 0 and r is not less than R => suff;

(2) is not suff.

GMAT TIGER · Answer

i should make a correction.

with the information provided, if x = m = 0 and all elements in A are 0, then r = R. 
with the information provided, if x = m and all element in a are not 0, then r < R cuz the sum of devation of the squares does not increase where as n increases. so r should be < R.

so it should be E rather than A.

Set A has n integers. Arithmetic mean is m. standard

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