NandishSS wrote:What is the standard deviation of a set of numbers whose mean is 20?
(1) The absolute value of the difference of each number in the set from the mean is equal
(2) The sum of the squares of the differences from the mean is greater than 100
OA:E
Source:Economist GMAT Tutor
We are asked to deduce SD, given that mean = 20.
S1: Case 1: Each element of the set = 20, so the set is: {... 20, 20, 20, ...}. The absolute value of the difference of each number from the mean = 0. Despite not knowing the number of terms in the set, we can conclude that SD = 0.
Case 2: No element of the set = 20, but its mean = 20. Say there are 2n number of elements in the set: n number of elements = (20 - x) and another n number of elements = (20 + x). Thus, the absolute value of the difference of each number from the mean = x. Since we do not know the value of x, S1 is insufficient.
S2: The falls under Case 2 of S1. All it states that 2n*x^2 > 100.
We know that standard deviation is the mean of squared deviations.
SD = [(Sum of the squares of the differences)/ number of terms]^(1/2) = [(2n*x^2)/2n]^(1/2) = [x^2]^(1/2) = x. Since we do not know the value of x, S2 is insufficient.
S1 and S2: Since Case 2 is common for S1 and S2, we cannot get anything even after combining S1 and S2. Insufficient.
OA:
E
-Jay
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