Descriptive statistics – Standard Deviation

If m is the arithmetic mean (average) of 4 integers a, b, c, and d and s is the standard deviation of the 4 integers and s = , then is s > 0?

(1) m > a
(2) a + b + c + d = 0

Solution:

s will be zero only in two instances: (i) when all the elements in the set are the same, or (ii) the set contains only one element, which in this case is not possible. So, we need to check whether a, b, c, and d are the same integers.

Statement (1): m > a
The average will be equal to a, b, c, and d only when a = b = c = d. Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.
SUFFICIENT

Statement (2): a + b + c + d = 0
When a = b = c = d = 0, s = 0
When a = -4, b = 0, c = 0, and d = 4, s > 0
NOT sufficient

Answer: A